# 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

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topFezoui, 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 -

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## Citations in EuDML Documents

top- Serge Piperno, Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems
- Serge Piperno, Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems
- Ludovic Moya, Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell’s equations
- Ludovic Moya, Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell’s equations

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