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.
constants
impedance
reduced Basis Method
Maxwell's equations
discontinuous Galerkin
integral-equation
local regularization
posteriori error estimation
Mathematics
partial-differential-equations
electromagnetic scattering
approximation
conductor
field
Author
Kristin Kirchner
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
University of Gothenburg
K. Urban
University of Ulm
O. Zeeb
University of Ulm
Mathematical Modelling and Numerical Analysis
28227840 (ISSN) 28047214 (eISSN)
Vol. 50 6 1763-1787Subject Categories
Computational Mathematics
Signal Processing
Mathematical Analysis
DOI
10.1051/m2an/2016006