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

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, 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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SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2009, 31 (3), pp.1985-2014. 〈10.1137/070709414〉
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Julien Diaz, Marcus Grote. Energy Conserving Explicit Local Time-Stepping for Second-Order Wave Equations. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2009, 31 (3), pp.1985-2014. 〈10.1137/070709414〉. 〈inria-00409233〉

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