Geodesic
Maxwell’s equations for conductors with impedance boundary conditions: Discontinuous Galerkin and Reduced Basis Methods
Kirchner, Kristin1 ; Urban, Karsten2 ; Zeeb, Oliver2
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

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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.

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DOI : 10.1051/m2an/2016006
Classification : 35Q61, 65N30, 65N15
Keywords: Maxwell’s equations, impedance, conductor, discontinuous Galerkin, Reduced Basis Method

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. 
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     title = {Maxwell{\textquoteright}s equations for conductors with impedance boundary conditions: {Discontinuous} {Galerkin} and {Reduced} {Basis} {Methods}},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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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

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