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; Serge Piperno

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • 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 39.6 (2010): 1149-1176. <http://eudml.org/doc/194300>.

@article{Fezoui2010,
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. },
author = {Fezoui, Loula, Lanteri, Stéphane, Lohrengel, Stéphanie, Piperno, Serge},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Electromagnetics; finite volume methods; discontinuous Galerkin methods; centered fluxes; leap-frog time scheme; L2 stability; unstructured meshes; absorbing boundary condition; convergence; divergence preservation.; electromagnetics; discontinuous Galerkin methods},
language = {eng},
month = {3},
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/194300},
volume = {39},
year = {2010},
}

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
DA - 2010/3//
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; L2 stability; unstructured meshes; absorbing boundary condition; convergence; divergence preservation.; electromagnetics; discontinuous Galerkin methods
UR - http://eudml.org/doc/194300
ER -

References

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