Weighted Regularization of Maxwell Equations – Computations in Curvilinear Polygons

The problem consists in finding the non-zero frequencies ω> 0 such that there exists an electromagnetic field (E,H) = 0 solving the equation curl εE − iω µH = 0 and curlµH + iω εE = 0 in Ω, (1) in the cavity Ω. We assume perfect conductor boundary conditions, that is E×n = 0 and H ·n = 0 on ∂Ω, where n denotes the outer unit normal on ∂Ω. Concentrating on the problems posed by the singularities of the boundary of Ω, we assume that the dielectric material filling Ω is homogeneous and isotropic, that is, after a possible change of unknowns ε = µ = 1. We want to solve (1) by a Galerkin procedure. The first step is to propose a variational formulation for (1). Eliminating H from the equations, we find the formulatio