A numerical method to solve Maxwell’s equations in 3D singular geometry

Abstract

We propose a new method to solve the 3D Maxwell equations in axisymmetric singular domains, containing reentrant corner or edges. By doing a Fourier analysis, one arrives to a sequence of singular problems set in 2D domains, and 3D solutions are computed by solving 2D problems, depending on a Fourier mode 𝑘. For each 𝑘, the solution is decomposed into a regular and a singular part. The regular part is computed with a finite element method. The singular part belongs to a finite-dimensional subspace and is computed by an appropriate numerical approach, only for the modes 𝑘 = 0, ±1, 2. The total the solution is then reconstructed, based on a non stationary variational formulation. Numerical examples will be shown.