Uniqueness of an inverse electromagnetic coefficient problem with partial boundary data and its numerical resolution through an iterated sensitivity equation

TL;DR

This paper establishes uniqueness and proposes a numerical method for reconstructing internal perturbations in a medium's refractive index from partial boundary electromagnetic data, advancing inverse Maxwell problem solutions.

Contribution

It provides a new uniqueness proof and a comprehensive numerical reconstruction procedure using an iterated sensitivity equation for inverse Maxwell problems.

Findings

Proved uniqueness of the inverse problem with partial boundary data.

Developed a numerical reconstruction method based on sensitivity equations.

Demonstrated the effectiveness of the approach through simulations.

Abstract

In this paper we study an inverse boundary value problem for Maxwell's equations. The goal is to reconstruct perturbations in the refractive index of the medium inside an object from the knowledge of the tangential trace of an electric field on a part of the boundary of the domain. We first provide a uniqueness result for this inverse problem. Then, we propose a complete procedure to reconstruct numerically the perturbations, based on the minimization of a cost functional involving an iterated sensitivity equation.