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.
2 University of Ulm, Institute for Numerical Mathematics, Helmholtzstrasse 18, 89069 Ulm, Germany.
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
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