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

Abstract

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.