Lab Home | Phone | Search
Center for Nonlinear Studies  Center for Nonlinear Studies
 Home 
 People 
 Current 
 Affiliates 
 Alumni 
 Visitors 
 Students 
 Research 
 ICAM-LANL 
 Quantum 
 Publications 
 Publications 
 2007 
 2006 
 2005 
 2004 
 2003 
 2002 
 2001 
 2000 
 <1999 
 Conferences 
 Workshops 
 Sponsorship 
 Talks 
 Colloquia 
 Colloquia Archive 
 Seminars 
 Postdoc Seminars Archive 
 Quantum Lunch 
 CMS Colloquia 
 Q-Mat Seminars 
 Q-Mat Seminars Archive 
 Archive 
 Kac Lectures 
 Dist. Quant. Lecture 
 Ulam Scholar 
 Colloquia 
 
 Jobs 
 Students 
 Summer Research 
 Student Application 
 Visitors 
 Description 
 Past Visitors 
 Services 
 General 
 PD Travel Request 
 
 History of CNLS 
 
 Maps, Directions 
 CNLS Office 
 T-Division 
 LANL 
 
Monday, September 12, 2011
1:00 PM - 2:00 PM
CNLS Conference Room (TA-3, Bldg 1690)

Postdoc Seminar

Adaptation of Mimetic Finite Difference discretizations to reducing the numerical dispersion in wave equations

Vitaliy Gyrya
T-5: APPLIED MATHEMATICS AND PLASMA PHYSICS

We are interested in a numerical solution of the acoustic wave equation (in the time domain) that is efficient and has small long-time integration error. There exists a large number of numerical schemes for solution of wave equations which are asymptotically accurate in the limit of infinite resolution. Unfortunately, in practice one always operates with finite resolution. As a consequence the numerical schemes may exhibit numerical anomalies behavior that is not observed in the physical problem. For the wave equation the typical anomalies, and the main source of long integration error, are numerical dispersion and anisotropy the phenomena predicting different speed of wave propagation depending on their wavelength and orientation. In contrast, in the underlying physical problem the propagation speed is constant for waves with all wavelengths moving in all directions. If the numerical dispersion is strong enough or the integration times are long enough, the wave profiles predicted by the numerical solutions may have very little resemblance with the physical ones. We present an adaptation technique, based on the Mimetic Finite Difference (MFD) discretizations, that allows to minimize the numerical anomalies such as numerical dispersion and anisotropy. The numerical experiments show that the proposed method is consistently better than the classical methods for reducing long-time integration error. The typical L2-error is an order of magnitude smaller for the proposed method. No prior knowledge of MFD methods is required. Familiarity with the classical Finite Element methods will be a plus, but is not a requirement either.

Host: Humberto C Godinez Vazquez, Mathematical Modeling and Analysis Theoretical Division, 5-9188