Modal computation for an open electromagnetic eigenvalue problem (Augustin Leclerc, INSA Rouen)

The study of electromagnetic (EM) wave propagation is essential for investigating the impact of human technologies on the environment. For example offshore wind energy is transported by dynamic twisted cables, whose armouring prevents the propagation of a significant proportion of the waves. Nevertheless, what remains escapes from the cable, and our aim here is to study its diffusion in the vast expanse of sea water.

To consider this problem, we propose to model the cable and the surrounding water by an open 3D waveguide, which is an invariant domain according to the cable direction and which is unbounded in the two other directions. Hence, we will take a modal approach for the resolution, with absorbing boundary conditions (ABC) around the section of the cable.

First, we present the simplified model of open Helmoltz eigenproblem. Especially, we will discuss how to efficiently linearize the ABC w.r.t. the eigenvalue. Then, we will consider the adaptation of the boundary condition to the Maxwell eigenproblem.