Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes

Loula Fezoui; Stéphane Lanteri; Stéphanie Lohrengel[1]; Serge Piperno

  • [1] Dieudonné Lab., UNSA, UMR CNRS 6621, Parc Valrose, 06108 Nice Cedex 2, France.

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2005)

  • Volume: 39, Issue: 6, page 1149-1176
  • ISSN: 0764-583X

Abstract

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A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved for metallic cavities. Convergence is proved for ℙ k Discontinuous elements on tetrahedral meshes, as well as a discrete divergence preservation property. Promising numerical examples with low-order elements show the potential of the method.

How to cite

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Fezoui, Loula, et al. "Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.6 (2005): 1149-1176. <http://eudml.org/doc/244803>.

@article{Fezoui2005,
abstract = {A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved for metallic cavities. Convergence is proved for $\mathbb \{P\}_k$ Discontinuous elements on tetrahedral meshes, as well as a discrete divergence preservation property. Promising numerical examples with low-order elements show the potential of the method.},
affiliation = {Dieudonné Lab., UNSA, UMR CNRS 6621, Parc Valrose, 06108 Nice Cedex 2, France.},
author = {Fezoui, Loula, Lanteri, Stéphane, Lohrengel, Stéphanie, Piperno, Serge},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {electromagnetics; finite volume methods; discontinuous Galerkin methods; centered fluxes; leap-frog time scheme; $L^2$ stability; unstructured meshes; absorbing boundary condition; convergence; divergence preservation},
language = {eng},
number = {6},
pages = {1149-1176},
publisher = {EDP-Sciences},
title = {Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes},
url = {http://eudml.org/doc/244803},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Fezoui, Loula
AU - Lanteri, Stéphane
AU - Lohrengel, Stéphanie
AU - Piperno, Serge
TI - Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 6
SP - 1149
EP - 1176
AB - A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved for metallic cavities. Convergence is proved for $\mathbb {P}_k$ Discontinuous elements on tetrahedral meshes, as well as a discrete divergence preservation property. Promising numerical examples with low-order elements show the potential of the method.
LA - eng
KW - electromagnetics; finite volume methods; discontinuous Galerkin methods; centered fluxes; leap-frog time scheme; $L^2$ stability; unstructured meshes; absorbing boundary condition; convergence; divergence preservation
UR - http://eudml.org/doc/244803
ER -

References

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