Maxwell's equations for conductors with impedance boundary conditions: Discontinuous Galerkin and Reduced Basis Methods
Journal article, 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. 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
Maxwell's equations
electromagnetic scattering
conductor
reduced Basis Method
constants
posteriori error estimation
local regularization
impedance
partial-differential-equations
field
integral-equation
approximation
discontinuous Galerkin
Author
Kristin Kirchner
University of Gothenburg
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
K. Urban
Universitat Ulm
O. Zeeb
Universitat Ulm
Mathematical Modelling and Numerical Analysis
0764-583X (ISSN) 1290-3841 (eISSN)
Vol. 50 6 1763-1787Subject Categories (SSIF 2011)
Computational Mathematics
Signal Processing
Mathematical Analysis
DOI
10.1051/m2an/2016006