Finite Element Method for Approximating Electro-Magnetic Scattering from a Conducting Object
Date
2000
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
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 Poincare-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.