Maxwell’s equations for conductors with impedance boundary conditions: Discontinuous Galerkin and Reduced Basis Methods

Kirchner, Kristin; Urban, Karsten; Zeeb, Oliver

doi:10.1051/m2an/2016006

Kirchner, Kristin ¹ ; Urban, Karsten ² ; Zeeb, Oliver ²

¹ Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Gothenburg, Sweden.
² University of Ulm, Institute for Numerical Mathematics, Helmholtzstrasse 18, 89069 Ulm, Germany.

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 6, pp. 1763-1787.

Résumé

We consider Maxwell’s equations with impedance boundary conditions on a conductive polyhedron with polyhedral holes. Well-posedness of the variational formulation is proven, a hp-discontinuous Galerkin (hp-dG) approximation as well as a priori error estimates are introduced. Next, we use the frequency $ω$ as a parameter in a multi-query context. For this purpose, we derive a Reduced Basis Method (RBM) based upon the dG formulation as well as the corresponding a posteriori error bound. Numerical results indicate the efficiency and the robustness of the scheme.

Reçu le : 2015-07-02
Accepté le : 2016-01-22

MR Zbl

DOI : 10.1051/m2an/2016006

Classification : 35Q61, 65N30, 65N15
Mots-clés : Maxwell’s equations, impedance, conductor, discontinuous Galerkin, Reduced Basis Method

Affiliations des auteurs :

Kirchner, Kristin ¹ ; Urban, Karsten ² ; Zeeb, Oliver ²

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     author = {Kirchner, Kristin and Urban, Karsten and Zeeb, Oliver},
     title = {Maxwell{\textquoteright}s equations for conductors with impedance boundary conditions: {Discontinuous} {Galerkin} and {Reduced} {Basis} {Methods}},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1763--1787},
     publisher = {EDP-Sciences},
     volume = {50},
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     mrnumber = {3580121},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/m2an/2016006/}
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Kirchner, Kristin; Urban, Karsten; Zeeb, Oliver. Maxwell’s equations for conductors with impedance boundary conditions: Discontinuous Galerkin and Reduced Basis Methods. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 6, pp. 1763-1787. doi : 10.1051/m2an/2016006. http://archive.numdam.org/articles/10.1051/m2an/2016006/

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