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

Julien Diaz 1 Marcus Grote 2
1 MAGIQUE-3D - Advanced 3D Numerical Modeling in Geophysics
INRIA Futurs, UPPA - Université de Pau et des Pays de l'Adour, CNRS - Centre National de la Recherche Scientifique
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 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.
Type de document :
[Research Report] RR-6377, INRIA. 2007, pp.34
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Soumis le : lundi 3 décembre 2007 - 10:37:32
Dernière modification le : jeudi 11 janvier 2018 - 06:19:48
Document(s) archivé(s) le : mardi 21 septembre 2010 - 15:10:00


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  • HAL Id : inria-00193160, version 2



Julien Diaz, Marcus Grote. Energy Conserving Explicit Local Time-Stepping for Second-Order Wave Equations. [Research Report] RR-6377, INRIA. 2007, pp.34. 〈inria-00193160v2〉



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