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v1 (30-11-2007)

v2 (03-12-2007)

Energy Conserving Explicit Local Time-Stepping for Second-Order Wave Equations

Julien Diaz 1, Marcus J. Grote 2

(2007)

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 symmetric finite element discretization in space with an essentially diagonal mass matrix, the resulting discrete numerical scheme is explicit, inherently parallel, and exactly conserves a discrete energy. Starting from the standard second-order ``leap-frog'' scheme, time-stepping methods of arbitrary order of accuracy are derived. Numerical experiments illustrate the efficiency and usefulness of these methods and validate the theory.

1 :	MAGIQUE-3D (INRIA Futurs)
	INRIA – CNRS – Université de Pau et des Pays de l'Adour [UPPA]
2 :	Department of Mathematics [Basel]
	Université de Bâle – Universität Basel

Domaine

:

Mathématiques/Equations aux dérivées partielles Mathématiques/Analyse numérique

Mots-clés : Second-order hyperbolic problems – explicit methods – time reversible methods – energy conservation – discontinuous Galerkin methods – finite element methods – mass lumping – wave equation – acoustic waves – electromagnetic waves – elastic waves

inria-00193160, version 2

http://hal.inria.fr/inria-00193160

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Soumis le : Lundi 3 Décembre 2007, 10:37:32

Dernière modification le : Lundi 3 Décembre 2007, 10:38:12