Electromagnetics - Modelling, Simulation, Control and Industrial Applications - Abstract

Hohage, Thorsten

A spectrally accurate method for the forward and inverse dielectric obstacle scattering problem

We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations. For the numerical solution of these coupled integral equations we propose a fast spectral algorithm by transporting these equations onto the unit sphere. We review the differentiability properties of the boundary to far field operator and give a characterization of the adjoint operator of the first Fréchet derivative. These results are used to solve the inverse problem by a Newton-type method. (joint work with Frédérique Le Louër)