Optimization approach for the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions from limited observations

TL;DR

This paper presents an optimization-based method for reconstructing dielectric permittivity and magnetic permeability in 3D Maxwell's equations using limited boundary data, supported by theoretical stability via Carleman estimates.

Contribution

It introduces a novel hybrid finite element/difference approach for simultaneous reconstruction of electromagnetic parameters with theoretical stability guarantees.

Findings

Successful numerical reconstruction demonstrated

Theoretical stability established via Carleman estimates

Effective handling of limited boundary observations

Abstract

We consider the inverse problem of the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions of the Maxwell's system in 3D with limited boundary observations of the electric field. The theoretical stability for the problem is provided by the Carleman estimates. For the numerical computations the problem is formulated as an optimization problem and hybrid finite element/difference method is used to solve the parameter identification problem.