Monique Dauge (Rennes. France)

Computation of resonance frequencies for Maxwell equations in non smooth domains

Abstract

We are interested in the computation by finite elements of the non-zero eigenvalues of the (curl, curl) bilinear form with perfect conductor boundary conditions, or impedance boundary conditions. After a brief review of different formulations using a Galerkin approximation by edge elements, we concentrate our attention on methods based on a regularization of the (curl, curl) form, which allow the elimination of the big kernel constituted by the gradients. We explain the reasons why such a method can be illusive in a domain having reentrant corners or edges. We describe two types of strategies to overcome the apparent obstruction to the regularization method. We quote methods consisting in adding singular functions or computing them apart, and we develop the method of regularization with weight, consisting in regularizing the (curl, curl) form by a (div,div) bilinear form, where the standard uniform measure is changed into a weighted measure, where the weight behaves like the distance to the reentrant corners or edges.