Mikhail Shashkov's Page

Mikhail Shashkov
Theoretical Division , Group T-7, MS-B284
Los Alamos National Laboratory
Los Alamos NM 87545, U.S.A.
Voice: 505.667.4400
FAX: 505.665.5757
shashkov@lanl.gov

Cell

Ph.D. - Keldysh Institute of Applied Mathematics, Moscow, Russia - 1979
Habilitation - Moscow State University, Moscow, Russia - 1991

My Book

M. Shashkov, Conservative Finite-Difference Methods on General Grids,
CRC Press, Boca Raton, Fl, 1996, 359 pages + Disc. How to order <-----> How to order

Recent Publications:

J. Castillo, J.M.Hyman, M. Shashkov and S.Steinberg, The Sensitivity and Accuracy of Fourth Order Finite-Difference Schemes on Nonuniform Grids in One Dimension, An International Journal of Computers & Mathematics with Applications, Vol. 30, No. 8, pp. 41-55, 1995. --(pdf) J. Castillo, J.M.Hyman, M. Shashkov and S.Steinberg, High-Order Mimetic Finite Difference Methods on Nonuniform Grids, in ICOSAHOM-95, Proc. of the Third International Conference on Spectral and High Order Methods, Houston, Texas, 5-9 June 1995. Special Issue of Houston Journal of Mathematics, eds. A.V. Ilin and L. R. Scott, 1995, pp. 347-361. --(ps) M. Shashkov and S. Steinberg, Solving Diffusion Equations with Rough Coefficients in Rough Grids, Journal of Computational Physics, 129, pp. 383-405, (1996). --- (pdf) J. Hyman, M. Shashkov and S. Steinberg, The Numerical Solution of Diffusion Problems in Strongly Heterogenous Non-Isotropic Materials, Journal of Computational Physics, 132, pp. 130-148, (1997). --- (pdf) J. M. Hyman and M. Shashkov, Natural Discretizations for the Divergence, Gradient, and Curl on Logically Rectangular Grids, International Journal of Computers & Mathematics with Applications, Vol. 33, No. 4, 1997, pp. 81-104. --- (pdf) J. M. Hyman and M. Shashkov, Adjoint Operators for the Natural Discretizations of the Divergence, Gradient and Curl on Logically Rectangular Grids, Applied Numerical Mathematics 25 (1997) 413-442. -- (ps) J. M. Hyman and M. Shashkov, The Approximation of Boundary Conditions for Mimetic Finite Difference Methods, Computers & Mathematics with Applications, 36 (1998) pp. 79--99. -- (pdf) M. Shashkov, B. Swartz and B. Wendroff, Local Reconstruction of a Vector Field from its Components on the Faces of Grid Cells, Journal of Computational Physics, 139, pp. 406--409, (1998). --(pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, LA-UR-98-1032. --(ps) E. J. Caramana and M. Shashkov, Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagarangian Subzonal Masses and Pressures, Journal of Computational Physics, 142, pp. 521--561, (1998). --(pdf) J. M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion, in J.~A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, 1998) 561--563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998, --(ps) E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Castillo, J.M.Hyman, M. Shashkov and S.Steinberg, High-Order Mimetic Finite Difference Methods on Nonuniform Grids, in ICOSAHOM-95, Proc. of the Third International Conference on Spectral and High Order Methods, Houston, Texas, 5-9 June 1995. Special Issue of Houston Journal of Mathematics, eds. A.V. Ilin and L. R. Scott, 1995, pp. 347-361. --(ps) M. Shashkov and S. Steinberg, Solving Diffusion Equations with Rough Coefficients in Rough Grids, Journal of Computational Physics, 129, pp. 383-405, (1996). --- (pdf) J. Hyman, M. Shashkov and S. Steinberg, The Numerical Solution of Diffusion Problems in Strongly Heterogenous Non-Isotropic Materials, Journal of Computational Physics, 132, pp. 130-148, (1997). --- (pdf) J. M. Hyman and M. Shashkov, Natural Discretizations for the Divergence, Gradient, and Curl on Logically Rectangular Grids, International Journal of Computers & Mathematics with Applications, Vol. 33, No. 4, 1997, pp. 81-104. --- (pdf) J. M. Hyman and M. Shashkov, Adjoint Operators for the Natural Discretizations of the Divergence, Gradient and Curl on Logically Rectangular Grids, Applied Numerical Mathematics 25 (1997) 413-442. -- (ps) J. M. Hyman and M. Shashkov, The Approximation of Boundary Conditions for Mimetic Finite Difference Methods, Computers & Mathematics with Applications, 36 (1998) pp. 79--99. -- (pdf) M. Shashkov, B. Swartz and B. Wendroff, Local Reconstruction of a Vector Field from its Components on the Faces of Grid Cells, Journal of Computational Physics, 139, pp. 406--409, (1998). --(pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, LA-UR-98-1032. --(ps) E. J. Caramana and M. Shashkov, Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagarangian Subzonal Masses and Pressures, Journal of Computational Physics, 142, pp. 521--561, (1998). --(pdf) J. M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion, in J.~A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, 1998) 561--563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998, --(ps) E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Shashkov and S. Steinberg, Solving Diffusion Equations with Rough Coefficients in Rough Grids, Journal of Computational Physics, 129, pp. 383-405, (1996). --- (pdf) J. Hyman, M. Shashkov and S. Steinberg, The Numerical Solution of Diffusion Problems in Strongly Heterogenous Non-Isotropic Materials, Journal of Computational Physics, 132, pp. 130-148, (1997). --- (pdf) J. M. Hyman and M. Shashkov, Natural Discretizations for the Divergence, Gradient, and Curl on Logically Rectangular Grids, International Journal of Computers & Mathematics with Applications, Vol. 33, No. 4, 1997, pp. 81-104. --- (pdf) J. M. Hyman and M. Shashkov, Adjoint Operators for the Natural Discretizations of the Divergence, Gradient and Curl on Logically Rectangular Grids, Applied Numerical Mathematics 25 (1997) 413-442. -- (ps) J. M. Hyman and M. Shashkov, The Approximation of Boundary Conditions for Mimetic Finite Difference Methods, Computers & Mathematics with Applications, 36 (1998) pp. 79--99. -- (pdf) M. Shashkov, B. Swartz and B. Wendroff, Local Reconstruction of a Vector Field from its Components on the Faces of Grid Cells, Journal of Computational Physics, 139, pp. 406--409, (1998). --(pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, LA-UR-98-1032. --(ps) E. J. Caramana and M. Shashkov, Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagarangian Subzonal Masses and Pressures, Journal of Computational Physics, 142, pp. 521--561, (1998). --(pdf) J. M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion, in J.~A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, 1998) 561--563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998, --(ps) E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Hyman, M. Shashkov and S. Steinberg, The Numerical Solution of Diffusion Problems in Strongly Heterogenous Non-Isotropic Materials, Journal of Computational Physics, 132, pp. 130-148, (1997). --- (pdf) J. M. Hyman and M. Shashkov, Natural Discretizations for the Divergence, Gradient, and Curl on Logically Rectangular Grids, International Journal of Computers & Mathematics with Applications, Vol. 33, No. 4, 1997, pp. 81-104. --- (pdf) J. M. Hyman and M. Shashkov, Adjoint Operators for the Natural Discretizations of the Divergence, Gradient and Curl on Logically Rectangular Grids, Applied Numerical Mathematics 25 (1997) 413-442. -- (ps) J. M. Hyman and M. Shashkov, The Approximation of Boundary Conditions for Mimetic Finite Difference Methods, Computers & Mathematics with Applications, 36 (1998) pp. 79--99. -- (pdf) M. Shashkov, B. Swartz and B. Wendroff, Local Reconstruction of a Vector Field from its Components on the Faces of Grid Cells, Journal of Computational Physics, 139, pp. 406--409, (1998). --(pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, LA-UR-98-1032. --(ps) E. J. Caramana and M. Shashkov, Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagarangian Subzonal Masses and Pressures, Journal of Computational Physics, 142, pp. 521--561, (1998). --(pdf) J. M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion, in J.~A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, 1998) 561--563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998, --(ps) E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. M. Hyman and M. Shashkov, Natural Discretizations for the Divergence, Gradient, and Curl on Logically Rectangular Grids, International Journal of Computers & Mathematics with Applications, Vol. 33, No. 4, 1997, pp. 81-104. --- (pdf) J. M. Hyman and M. Shashkov, Adjoint Operators for the Natural Discretizations of the Divergence, Gradient and Curl on Logically Rectangular Grids, Applied Numerical Mathematics 25 (1997) 413-442. -- (ps) J. M. Hyman and M. Shashkov, The Approximation of Boundary Conditions for Mimetic Finite Difference Methods, Computers & Mathematics with Applications, 36 (1998) pp. 79--99. -- (pdf) M. Shashkov, B. Swartz and B. Wendroff, Local Reconstruction of a Vector Field from its Components on the Faces of Grid Cells, Journal of Computational Physics, 139, pp. 406--409, (1998). --(pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, LA-UR-98-1032. --(ps) E. J. Caramana and M. Shashkov, Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagarangian Subzonal Masses and Pressures, Journal of Computational Physics, 142, pp. 521--561, (1998). --(pdf) J. M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion, in J.~A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, 1998) 561--563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998, --(ps) E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. M. Hyman and M. Shashkov, Adjoint Operators for the Natural Discretizations of the Divergence, Gradient and Curl on Logically Rectangular Grids, Applied Numerical Mathematics 25 (1997) 413-442. -- (ps) J. M. Hyman and M. Shashkov, The Approximation of Boundary Conditions for Mimetic Finite Difference Methods, Computers & Mathematics with Applications, 36 (1998) pp. 79--99. -- (pdf) M. Shashkov, B. Swartz and B. Wendroff, Local Reconstruction of a Vector Field from its Components on the Faces of Grid Cells, Journal of Computational Physics, 139, pp. 406--409, (1998). --(pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, LA-UR-98-1032. --(ps) E. J. Caramana and M. Shashkov, Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagarangian Subzonal Masses and Pressures, Journal of Computational Physics, 142, pp. 521--561, (1998). --(pdf) J. M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion, in J.~A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, 1998) 561--563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998, --(ps) E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. M. Hyman and M. Shashkov, The Approximation of Boundary Conditions for Mimetic Finite Difference Methods, Computers & Mathematics with Applications, 36 (1998) pp. 79--99. -- (pdf) M. Shashkov, B. Swartz and B. Wendroff, Local Reconstruction of a Vector Field from its Components on the Faces of Grid Cells, Journal of Computational Physics, 139, pp. 406--409, (1998). --(pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, LA-UR-98-1032. --(ps) E. J. Caramana and M. Shashkov, Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagarangian Subzonal Masses and Pressures, Journal of Computational Physics, 142, pp. 521--561, (1998). --(pdf) J. M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion, in J.~A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, 1998) 561--563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998, --(ps) E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. M. Hyman and M. Shashkov, The Approximation of Boundary Conditions for Mimetic Finite Difference Methods, Computers & Mathematics with Applications, 36 (1998) pp. 79--99. -- (pdf) M. Shashkov, B. Swartz and B. Wendroff, Local Reconstruction of a Vector Field from its Components on the Faces of Grid Cells, Journal of Computational Physics, 139, pp. 406--409, (1998). --(pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, LA-UR-98-1032. --(ps) E. J. Caramana and M. Shashkov, Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagarangian Subzonal Masses and Pressures, Journal of Computational Physics, 142, pp. 521--561, (1998). --(pdf) J. M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion, in J.~A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, 1998) 561--563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998, --(ps) E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Shashkov, B. Swartz and B. Wendroff, Local Reconstruction of a Vector Field from its Components on the Faces of Grid Cells, Journal of Computational Physics, 139, pp. 406--409, (1998). --(pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, LA-UR-98-1032. --(ps) E. J. Caramana and M. Shashkov, Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagarangian Subzonal Masses and Pressures, Journal of Computational Physics, 142, pp. 521--561, (1998). --(pdf) J. M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion, in J.~A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, 1998) 561--563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998, --(ps) E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, LA-UR-98-1032. --(ps) E. J. Caramana and M. Shashkov, Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagarangian Subzonal Masses and Pressures, Journal of Computational Physics, 142, pp. 521--561, (1998). --(pdf) J. M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion, in J.~A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, 1998) 561--563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998, --(ps) E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
E. J. Caramana and M. Shashkov, Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagarangian Subzonal Masses and Pressures, Journal of Computational Physics, 142, pp. 521--561, (1998). --(pdf) J. M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion, in J.~A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, 1998) 561--563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998, --(ps) E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion, in J.~A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, 1998) 561--563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998, --(ps) E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulation of Artificial Viscosity for Multi-dimensional Shock Wave Computations, Journal of Computational Physics, 144, pp. 70-97, (1998). --(pdf) J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf) E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
E. J. Caramana, D. E. Burton, M. J. Shashkov, and P. P. Whalen, The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy, Journal of Computational Physics, 146, pp. 227--262, (1998). --(pdf) R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Liska, M. Shashkov and B. Swartz, Smoothly Blending Circular Interpolants in Two and Three Dimensions, LA-UR-98-4969, Journal of Computer Aided Geometric Design, submitted. --(ps) L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
L. Margolin and M. Shashkov, Using a Curvilinear Grid to Construct Symmetry-Preserving Discretization for Lagrangian Gas Dynamics, Journal of Computational Physics, 149, pp.389--417, (1999) --pdf J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf) M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Shashkov and B. Wendroff, A Composite Scheme for Gas Dynamics in Lagrangian Coordinates, Journal of Computational Physics, 150, pp. 502--517 (1999). -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf) L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
L. Margolin, M. Shashkov and M. Taylor, Symmetry-Preserving Discretizations for Lagrangian Gas Dynamics, LA-UR-99-4358, To appear, Proceedings of ENUMATH99. -- (ps) J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Campbell and M. Shashkov, A Tensor Artifical Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-2290. -- (ps) Also Journal of Computational Physics, 172 (2001), pp.739--765. J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Campbell, M. Shashkov, The Compatible Lagrangian Hydrodynamics Algorithm on Unstructured Grids, LA-UR-00-3231, Submitted to Journal of Computational Physics. -- (ps) J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Castillo, J. Hyman, M. Shashkov, and S. Steinberg, Fourth and Sixth-Order Conservatve Finite Difference Approximations of the Divergence and Gradient, LA-UR-99-5059, To appear at An IMACS Journal on Applied Numerical Mathematics. -- (ps) L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
L. Margolin, M. Shashkov and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf) J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Campbell, M. Shashkov, A Tensor Artificial Viscosity Using a Mimetic Finite Difference Algorithm, LA-UR-00-4507, Submitted to Journal of Computational Physics. -- (ps) J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Hyman, S. Li, P. Knupp and M. Shashkov, An Algorithm for Aligning a Quadrilateral Grid with Internal Interfaces, Journal of Computational Physics, 163 (2000), pp. 133-149. -- (pdf) J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps) J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, LA-UR-01-1194, Submitted to Journal of Computational Physics. -- (ps) J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf) J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps). M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Shashkov and P. Knupp Optimization-Based Reference Matrix Rezone Strategies for Arbitrary Lagrangian Eulerian Methods on Unstructured Grids, LA-UR-01-2948. Proceedings of 10th International Roundtable, October, 2001, submitted to Journal of Engineering with Computers. -- (ps) M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps) R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps) J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps) P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
P. Knupp, L. Margolin and M. Shashkov, Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 176 (2002) p.93-128. -- (ps) L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
L. G. Margolin and M. Shashkov, Second-Order Sign-Preserving Remapping on General Grids, LA-UR-02-525. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-0945, Submitted to the 8-th International Conference on Numerical Grid Generation in Computational Fiel Simulations, June 3-6, 2002, Honolulu, Hawaii. -- (ps) R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Garimella, M. Shashkov, and P. Knupp, Quality Improvement of Surface Triangulations using Local Parametrization, LA-UR-02-2806, Submitted to the 11-th International Meshing Roundtable -- September 15-18,2002, Ithaca, New York, USA. -- (ps) J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps). V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
V. Ganzha, R. Liska, M. Shashkov and C. Zenger, Support operator method for Laplace equation on unstructured triangular grid, Selcuk J. Appl. Math. 3 (2002), 21-48. (ps). M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Shashkov and P. Knupp, Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes, Selcuk J. Appl. Math. 3 (2002), 81-99. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Kucharik, M. Shashkov and B. Wendroff, Efficient Second-Order Bound-Preserving Remapping (Conservative Interpolation), LA-UR-02-6395. (ps). M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Kucharik, M. Shashkov and B. Wendroff, Second-Order, Local-Bound-Preserving Remapping for ALE Methhods, LA-UR-02-5840, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Garimella, M. Shashkov and V. Dyadechko, Quality Improement of 3D Meshes in ALE Simlations of Gas Dynamics, LA-UR-02-6396, Submitted to Second MIT Conference on Computational Fluid and Solid Mechanics, June 2003, MIT, Cambridge, USA. J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf) R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Liska, M. Shashkov, and B. Wendroff, Lagrangian Composite Schemes on Triangular Unstructured Grids, LA-UR-02-7834, Proceedings of Confernce on "Mathematical and Computer Modelling in Science and Engineering, January 27-30, 2003, Prague, Czech Republic. R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Liska, M. Shashkov, and B. Swartz, Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolans, Selcuk J. Appl. Math. 3(2) (2002), 81-98. (ps). K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics. M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Berndt and M. Shashkov, Multilevel Accelerated Optimization for Problems in Grid Generation, LA-UR-03-3474, Proceeding of 12 Meshing Round Table. --- (ps) M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Kucharik, M. Shashkov, and B. Wendroff, An Efficient Linearity-and-Bound-Preserving Remapping Methods, Journal of Computational Physics, 188 (2003) pp. 462--471. R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Garimella, M. Kucharik, M. Shashkov, Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods, LA-UR-03-7609, Proceedings of The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2003), August 18-22, 2003, Prague, Czech Republic. Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
P. Bochev and M. Shashkov, Constrained Interpolation (Remap) of Divergence-Free Fields, LA-UR-03-7903, Submitted to Computer Methods in Applied Mechanics and Engineering. --- (pdf) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, LA-UR-03-6619, Submitted to Journal of Computational Physics. --- (ps) K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
K. Lipnikov and M. Shashkov, Arbitrary Lagrangian-Eulerian Method with Error-Minimization-Based Rezone Strategy for Burgers' Equation LA-UR-03-8241. --- (ps) M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904. --- (ps) M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Shashkov and B. Wendroff, The Repair Paradigm and Application to Conservation Laws, Journal of Computational Physics, 198 (2004), pp. 265---277. LA-UR-03-6619 ---(ps) P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
P. Vachal, R.V. Garimella and M. Shashkov, Untangling of 2D Meshes for ALE Simulations, Journal of Computational Physics, 196 (2004), pp. 627---644. --- pdf. R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Liska, M. Shashkov, and V. Ganzha, Analysis and Optimization of Inner Products for Mimetic Finite Difference Methods on Triangular Grid, Mathematics and Computers in Simulation, 67 (2004), pp. 55---66. --- (pdf) R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Garimella, M. Shashkov and P. Knupp, Triangular and Quadrilateral Surface Mesh Quality Optimization Using Local Parametrization, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 913--928, LA-UR-02-7190 --- (pdf) L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
L.G Margolin and M. Shashkov, Remapping, Recovery and Repair on Staggered Grid, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 4139--4155, LA-UR-03-2230, --- (ps) K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finiteic Finite Difference Methods for Diffusion Equations on Non-orthogonal Non-Conformal Meshes, Journal of Computational Physics, 199 (2004), pp. 589---597, --- (pdf) R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Garimella and M. Shashkov, Polygonal Surface Mesh Optimization, Engineering with Computers (2004) 20:265-272. --- (pdf) P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
P. Bochev and M. Shashkov, Constrained Interpolation (remap) of Divergence-free Fields, Computer Methods in Applied Mechanics and Engineering, 194 (2005), pp. 511--530, --- (pdf) R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Loubere and M. Shashkov, A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary Lagrangian Eulerian Methods, Journal of Computational Physics, 209 (2005), 105-138. --- (pdf) Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The Mimetic Finite Difference Method on Polygonal Meshes for Diffusion-Type Problems, Computational Geosciences, 8 (2004), 301-324. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, LA-UR-04-6310, Journal of Computational Physics, to appear. - (pdf) R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Garimella, M. Kucharik and M. Shashkov, An Efficient Linearity and Bound Preserving Conservative Interpolation (Remapping) on Polyhedral Meshes, LA-UR-05-6193, Submitted to Computers and Fluids (ps). R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Garimella, V. Dyadechko, B. Swartz and M. Shashkov, Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations, Proceedings of the 14th International Meshing Roundtable, September 11-14, 2005, San Diego, CA, USA, pp. 19-32, B. W. Hanks (Ed.) Springer, 2005; see also Report of Los Alamos National Lab - LA-UR-05-2935 (ps). M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler, and I. Yotov, A Mortar Mimetic Finite Difference Method on Non-Matching Grids, Numerische Mathematik (2005) DOI: 10.1007/s00211-005-0631-4, On line. --- (pdf) K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
K. Lipnikov, M. Shashkov, The Error-Minimization-based Rezone Strategy for Arbitrary Lagrangian-Eulerian Methods, Numerical Methods for Partial Differential Equations, (2005) DOI: 10.1002/num.20113, On line. --- (pdf) K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
K. Lipnikov, M. Shashkov, and D. Svyatskiy, The Mimetic Finite Difference Discretization of Diffusion Problem on Unstructured Polyhedral Meshes, Journal of Computational Physics 211 (2006), pp. 473-491. --- (pdf) V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
V. Dyadechko and M. Shashkov, Moment-of-Fluid Interface Reconstruction, LA-UR-05-7571, LANL Report --- (pdf) K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
K. Lipnikov and M. Shashkov, The Error-Minimization-Based Strategy for Moving Mesh Methods, Communications in Computational Physics, Vol. 1, No. 1, pp. 53--81. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, LAUR-05-8717, Report of Los Alamos National Laboratory --- (pdf) M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Berndt, K. Lipnikov, M. Shashkov, M.F. Wheeler and I. Yotov, Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1728--1749. --- (pdf) M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Berndt, K. Lipnikov, P. Vachal, and M. Shashkov, A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes, Communications in Mathematical Sciences, Vol. 3, No. 4, pp. 665-680. --- (pdf) L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
L.G. Margolin and M. Shashkov, MPDATA: Gauge transformation, limiters and monotonicity, International Journal for Numerical Methods in Fluids (in press:DOI: 10.1002/ftd.1070) --- (pdf) F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM J. Numer. Anal. 43 (2005), pp. 1872-1896. --- (pdf) V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
V. Gvozdev, Y. Kuznetsov and M. Shashkov, Mimetic Dinite-Difference Method for Diffusion Equations on Polyhedral Meshes with Mixed Cells, LANL Report, LA-UR-06-4596 --- (pdf) V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
V. Dyadechko and M. Shashkov, Multi-material Interface Reconstruction from the Moment Data, LANL Report, LA-UR-06-5846 --- (pdf) H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
H. Ahn and M. Shashkov, Multi-material Interface Reconstruction on Generalized Plolyhedral Meshes, LANL Report, LA-UR-07-0656 --- (pdf) K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
K. Lipnikov, M. Shashkov, D. Svyatskiy, Yu. Vassilevski, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, LANL Report, LA-UR-07-2886 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Q1/P0 Approach to Lagrangian Schock Hydrodynamics, SANDIA REPORT, SAND 2007-1423. --- (pdf) F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A New Discretization Methodology for Diffusion Problems on Generalized Polyhedral Meshes, Comput. Methods Appl. mech. Engrg., 196 (2007), pp. 3682-3692. --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Liska and M. Shashkov, Enforcing the Discrete Maximum Prinicple for Linear Finite Element Solutions of Elliptic Problems, LAUR-07-3949. --- (pdf) M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Kucharik and M. Shashkov, Extension of efficient, swept-intergration-based conservative remapping method for meshes with changing connectivity. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1577 (2007) --- (pdf) M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
M. Shashkov, Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1574 (2007) --- (pdf) L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
L. G. Margolin and M. Shashkov, Finite volume methods and the equations of finite scale: A mimetic approach. Int. J. Numer. Meth. in Fluids - DOI:10.1002/fld.1592G(2007) --- (pdf) R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Liska and M. Shashkov, Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems, Communications in Computational Physics, Vol.3, N0. 4, pp. 852--877. --- (pdf) R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
R. Loubere, M. Shashkov and B. Wendroff, Volume Consistency in a Staggered Lagrangian Hydrodynamics Scheme, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2008.01.006 --- (pdf) V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
V. Dyadechko and M. Shashkov, Reconstruction of Mutli-material Interfaces from Moment Data, J. Comput. Phys., (2008), doi:10.1016/j.jcp.2007.12.029 --- (pdf) G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
G. Scovazzi, E. Love, and M. Shashkov, A Multi-Scale Lagrangian Schock Hydrodynamics on Q1/P0 finite elements:Theoretical framework and two-dimensionalcomputations, Comput. Methods Appl. Mech. Engrg. 197 (2008) 1056-1079. --- (pdf) H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
H.T. Ahn, M. Shashkov and M.A. Christon, The Moment-of-Fluid Method in Action , LA-UR-07-6854, Los Alamos National Laboratory, 2007, submitted to the Communications in Numerical Methods in Engineering, and also to be presented at the Third Asian-Pacific Congress on Computational Mechanics (APCOM'07), Dec. 3-6, 2007, Kyoto, Japan --- (pdf) H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)
H.T. Ahn, M. Shashkov, Adaptive Moment-of-Fluid Method, LA-UR-08-2153, Los Alamos National Laboratory, 2008. --- (pdf)

Moscow State University

CMC

Faculty of Computational Mathematics
and Cybernetics

Cell

Colleagues:

Len Margolin Victor Ganzha Pavel Bochev Stanly Steinberg Burton Wendroff Richard Liska Jim Morel Philippe Pebay Pat Knupp Mac Hyman
Victor Ganzha Pavel Bochev Stanly Steinberg Burton Wendroff Richard Liska Jim Morel Philippe Pebay Pat Knupp Mac Hyman
Pavel Bochev Stanly Steinberg Burton Wendroff Richard Liska Jim Morel Philippe Pebay Pat Knupp Mac Hyman
Stanly Steinberg Burton Wendroff Richard Liska Jim Morel Philippe Pebay Pat Knupp Mac Hyman
Burton Wendroff Richard Liska Jim Morel Philippe Pebay Pat Knupp Mac Hyman
Richard Liska Jim Morel Philippe Pebay Pat Knupp Mac Hyman
Jim Morel Philippe Pebay Pat Knupp Mac Hyman
Philippe Pebay Pat Knupp Mac Hyman
Pat Knupp Mac Hyman
Mac Hyman

Mikhail Shashkov <shashkov@lanl.gov>

Last modified: April 11, 15.29.03 MDT 2008