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Title: Discontinuous Galerkin Methods and Local Time Stepping for Wave Propagation

Abstract

Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. To overcome that stability restriction, local time-stepping methods are developed, which allow arbitrarily small time steps precisely where small elements in the mesh are located. When combined with a discontinuous Galerkin finite element discretization in space, which inherently leads to a diagonal mass matrix, the resulting numerical schemes are fully explicit. Starting from the classical Adams-Bashforth multi-step methods, local time stepping schemes of arbitrarily high accuracy are derived. Numerical experiments validate the theory and illustrate the usefulness of the proposed time integration schemes.

Authors:
;  [1]
  1. University of Basel, Rheinsprung 21, CH-4051 Basel (Switzerland)
Publication Date:
OSTI Identifier:
21428591
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1281; Journal Issue: 1; Conference: ICNAAM 2010: International conference of numerical analysis and applied mathematics 2010, Rhodes (Greece), 19-25 Sep 2009; Other Information: DOI: 10.1063/1.3498381; (c) 2010 American Institute of Physics
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; ELECTROMAGNETIC RADIATION; FINITE ELEMENT METHOD; MASS; MATRICES; STABILITY; TIME DEPENDENCE; WAVE EQUATIONS; WAVE PROPAGATION; CALCULATION METHODS; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL SOLUTIONS; NUMERICAL SOLUTION; PARTIAL DIFFERENTIAL EQUATIONS; RADIATIONS; SIMULATION

Citation Formats

Grote, M. J., and Mitkova, T. Discontinuous Galerkin Methods and Local Time Stepping for Wave Propagation. United States: N. p., 2010. Web. doi:10.1063/1.3498381.
Grote, M. J., & Mitkova, T. Discontinuous Galerkin Methods and Local Time Stepping for Wave Propagation. United States. doi:10.1063/1.3498381.
Grote, M. J., and Mitkova, T. 2010. "Discontinuous Galerkin Methods and Local Time Stepping for Wave Propagation". United States. doi:10.1063/1.3498381.
@article{osti_21428591,
title = {Discontinuous Galerkin Methods and Local Time Stepping for Wave Propagation},
author = {Grote, M. J. and Mitkova, T.},
abstractNote = {Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. To overcome that stability restriction, local time-stepping methods are developed, which allow arbitrarily small time steps precisely where small elements in the mesh are located. When combined with a discontinuous Galerkin finite element discretization in space, which inherently leads to a diagonal mass matrix, the resulting numerical schemes are fully explicit. Starting from the classical Adams-Bashforth multi-step methods, local time stepping schemes of arbitrarily high accuracy are derived. Numerical experiments validate the theory and illustrate the usefulness of the proposed time integration schemes.},
doi = {10.1063/1.3498381},
journal = {AIP Conference Proceedings},
number = 1,
volume = 1281,
place = {United States},
year = 2010,
month = 9
}