Open AccessEnergy Conserving Explicit Local Time Stepping for Second-Order Wave Equations
Author(s) -
Julien Diaz,
Marcus J. Grote
Publication year - 2009
Publication title -
siam journal on scientific computing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.674
H-Index - 147
eISSN - 1095-7197
pISSN - 1064-8275
DOI - 10.1137/070709414
Subject(s) - discretization , mathematics , diagonal , polygon mesh , mass matrix , stability (learning theory) , time stepping , numerical analysis , spacetime , finite element method , discrete time and continuous time , matrix (chemical analysis) , wave equation , block matrix , space time , mathematical analysis , geometry , computer science , physics , statistics , materials science , eigenvalues and eigenvectors , quantum mechanics , machine learning , nuclear physics , neutrino , composite material , thermodynamics , chemical engineering , engineering
International audienceLocally 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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