| Issue |
ESAIM: M2AN
Volume 50, Number 6, November-December 2016
|
|
|---|---|---|
| Page(s) | 1763 - 1787 | |
| DOI | https://doi.org/10.1051/m2an/2016006 | |
| Published online | 18 October 2016 | |
Maxwell’s equations for conductors with impedance boundary conditions: Discontinuous Galerkin and Reduced Basis Methods∗
1 Department of Mathematical Sciences, Chalmers University of
Technology and University of Gothenburg, SE-412 96 Gothenburg, Sweden.
kristin.kirchner@chalmers.se
2 University of Ulm, Institute for Numerical Mathematics,
Helmholtzstrasse 18, 89069 Ulm, Germany.
karsten.urban@uni-ulm.de; oliver.zeeb@uni-ulm.de
Received:
2
July
2015
Revised:
30
November
2015
Accepted:
22
January
2016
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.
Mathematics Subject Classification: 35Q61 / 65N30 / 65N15
Key words: Maxwell’s equations / impedance / conductor / discontinuous Galerkin / Reduced Basis Method
© EDP Sciences, SMAI 2016
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