A higher order perturbation approach for electromagnetic scattering problems on random domains

TL;DR

This paper introduces a higher order perturbation method for analyzing electromagnetic scattering on randomly shaped perfect conductors, providing accurate mean field approximations through second shape derivatives and boundary integral equations.

Contribution

It develops a novel third order accurate perturbation approach for electromagnetic scattering on uncertain domains, including efficient boundary integral equation solutions.

Findings

Third order accuracy in perturbation approximation of scattered fields.

Effective boundary integral equation discretization and solution methods.

Numerical validation in three-dimensional scattering problems.

Abstract

We consider time-harmonic electromagnetic scattering problems on perfectly conducting scatterers with uncertain shape. Thus, the scattered field will also be uncertain. Based on the knowledge of the two-point correlation of the domain boundary variations around a reference domain, we derive a perturbation analysis for the mean of the scattered field. Therefore, we compute the second shape derivative of the scattering problem for a single perturbation. Taking the mean, this leads to an at least third order accurate approximation with respect to the perturbation amplitude of the domain variations. To compute the required second order correction term, a tensor product equation on the domain boundary has to be solved. We discuss its discretization and efficient solution using boundary integral equations. Numerical experiments in three dimensions are presented.