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Article Dans Une Revue SIAM Journal on Scientific Computing Année : 2009

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

Résumé

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, is 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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Dates et versions

inria-00409233 , version 1 (06-08-2009)

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Julien Diaz, Marcus J. Grote. Energy Conserving Explicit Local Time-Stepping for Second-Order Wave Equations. SIAM Journal on Scientific Computing, 2009, 31 (3), pp.1985-2014. ⟨10.1137/070709414⟩. ⟨inria-00409233⟩
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