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.
Accepted:
DOI: 10.1051/m2an/2016006
Keywords: Maxwell’s equations, impedance, conductor, discontinuous Galerkin, Reduced Basis Method
@article{M2AN_2016__50_6_1763_0, author = {Kirchner, Kristin and Urban, Karsten and Zeeb, Oliver}, title = {Maxwell{\textquoteright}s equations for conductors with impedance boundary conditions: {Discontinuous} {Galerkin} and {Reduced} {Basis} {Methods}}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1763--1787}, publisher = {EDP-Sciences}, volume = {50}, number = {6}, year = {2016}, doi = {10.1051/m2an/2016006}, zbl = {1355.35177}, mrnumber = {3580121}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2016006/} }
TY - JOUR AU - Kirchner, Kristin AU - Urban, Karsten AU - Zeeb, Oliver TI - Maxwell’s equations for conductors with impedance boundary conditions: Discontinuous Galerkin and Reduced Basis Methods JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1763 EP - 1787 VL - 50 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016006/ DO - 10.1051/m2an/2016006 LA - en ID - M2AN_2016__50_6_1763_0 ER -
%0 Journal Article %A Kirchner, Kristin %A Urban, Karsten %A Zeeb, Oliver %T Maxwell’s equations for conductors with impedance boundary conditions: Discontinuous Galerkin and Reduced Basis Methods %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1763-1787 %V 50 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016006/ %R 10.1051/m2an/2016006 %G en %F M2AN_2016__50_6_1763_0
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 , Volume 50 (2016) no. 6, pp. 1763-1787. doi : 10.1051/m2an/2016006. http://www.numdam.org/articles/10.1051/m2an/2016006/
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