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

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