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

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

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topPiperno, 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 -

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