A finite element method for approximating electromagnetic scattering from a conducting object |
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Authors: | Andreas Kirsch Peter Monk |
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Affiliation: | Mathematisches Institut II, Universit?t Karlsruhe (TH), Englerstr. 2, D-76128 Karlsruhe, Germany; e-mail: Andreas.Kirsch@math.uni-karlsruhe.de, DE
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Abstract: | We provide an error analysis of a fully discrete finite element – Fourier series method for approximating Maxwell's equations. The problem is to approximate the electromagnetic field scattered by a bounded, inhomogeneous and anisotropic body. The method is to truncate the domain of the calculation using a series solution of the field away from this domain. We first prove a decomposition for the Poincaré-Steklov operator on this boundary into an isomorphism and a compact perturbation. This is proved using a novel argument in which the scattering problem is viewed as a perturbation of the free space problem. Using this decomposition, and edge elements to discretize the interior problem, we prove an optimal error estimate for the overall problem. |
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