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 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.
Mots-clés : electromagnetics, finite volume methods, discontinuous Galerkin methods, centered fluxes, leap-frog time scheme, $L^2$ stability, unstructured meshes, absorbing boundary condition, convergence, divergence preservation
@article{M2AN_2005__39_6_1149_0,
author = {Fezoui, Loula and Lanteri, St\'ephane and Lohrengel, St\'ephanie and Piperno, Serge},
title = {Convergence and stability of a discontinuous {Galerkin} time-domain method for the {3D} heterogeneous {Maxwell} equations on unstructured meshes},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1149--1176},
publisher = {EDP-Sciences},
volume = {39},
number = {6},
year = {2005},
doi = {10.1051/m2an:2005049},
mrnumber = {2195908},
zbl = {1094.78008},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2005049/}
}
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: Modélisation mathématique et analyse numérique PY - 2005 SP - 1149 EP - 1176 VL - 39 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005049/ DO - 10.1051/m2an:2005049 LA - en ID - M2AN_2005__39_6_1149_0 ER -
%0 Journal Article %A Fezoui, Loula %A Lanteri, Stéphane %A Lohrengel, Stéphanie %A Piperno, Serge %T Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 1149-1176 %V 39 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005049/ %R 10.1051/m2an:2005049 %G en %F M2AN_2005__39_6_1149_0
Fezoui, Loula; Lanteri, Stéphane; Lohrengel, Stéphanie; Piperno, Serge. Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 6, pp. 1149-1176. doi : 10.1051/m2an:2005049. http://www.numdam.org/articles/10.1051/m2an:2005049/
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