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Wednesday, March 19, 2008
2:00 PM - 3:00 PM
CNLS Conference Room (TA-3, Bldg 1690)


Theory and Algorithms for the Quasicontinuum Method

Mitchell Luskin
School of Mathematics, University of Minnesota

The quasicontinuum approximation is a method to reduce the atomistic degrees of freedom of a crystalline solid by piecewise linear interpolation from representative atoms. The coarsened triangles can be further approximated by a strain energy density based on the Cauchy-Born rule to obtain the finite element approximation in the continuum region. The forces on all of the representative atoms are determined except for those representative atoms in an atomistic-continuum interfacial region, where it is not known how to model the forces to simultaneously satisfy conditions of accuracy, efficiency, and conservation. We will present a theoretical framework for evaluating the goal- oriented accuracy of the atomistic-continuum interface, and we will apply this theory to analyze several quasicontinuum approximations. We will also present an a posteriori goal-oriented error estimator and a corresponding adaptive atomistic-continuum modeling and mesh refinement algorithm to enable a quantity of interest to be efficiently computed to a predetermined accuracy. Joint with Marcel Arndt and Matthew Dobson.

Host: Pieter Swart, T-07