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

Serge Piperno

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2006)

  • Volume: 40, Issue: 5, page 815-841
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Piperno, Serge. "Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 40.5 (2006): 815-841. <http://eudml.org/doc/245870>.

@article{Piperno2006,
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.},
author = {Piperno, Serge},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {waves; acoustics; Maxwell’s system; discontinuous Galerkin methods; symplectic schemes; energy conservation; second-order accuracy},
language = {eng},
number = {5},
pages = {815-841},
publisher = {EDP-Sciences},
title = {Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems},
url = {http://eudml.org/doc/245870},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Piperno, Serge
TI - Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2006
PB - EDP-Sciences
VL - 40
IS - 5
SP - 815
EP - 841
AB - 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.
LA - eng
KW - waves; acoustics; Maxwell’s system; discontinuous Galerkin methods; symplectic schemes; energy conservation; second-order accuracy
UR - http://eudml.org/doc/245870
ER -

References

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