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Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems

Published online by Cambridge University Press:  16 January 2007

Serge Piperno
Serge Piperno*
Affiliation:
Cermics, project-team caiman, École des Ponts, ParisTech, INRIA, France.
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Abstract

The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handle easily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh, calls for the construction of local-time stepping algorithms. These schemes have already been developed for N-body mechanical problems and are known as symplectic schemes. They are applied here to DGTD methods on wave propagation problems.

Keywords

WavesacousticsMaxwell's systemDiscontinuous Galerkin methodssymplectic schemesenergy conservationsecond-order accuracy.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 5 , September 2006 , pp. 815 - 841
Copyright
© EDP Sciences, SMAI, 2007

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