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.
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Submitted on : Monday, December 3, 2007 - 10:37:32 AM
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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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