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

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.
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https://hal.inria.fr/inria-00193160
Contributor : Rapport de Recherche Inria <>
Submitted on : Monday, December 3, 2007 - 10:37:32 AM
Last modification on : Friday, January 15, 2021 - 9:23:05 AM
Long-term archiving on: : Tuesday, September 21, 2010 - 3:10:00 PM

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RR-6377.pdf
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• HAL Id : inria-00193160, version 2

### Citation

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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