The factorization method for a defective region in an anisotropic material

TL;DR

This paper develops a factorization method to reconstruct defective regions within anisotropic materials using inverse acoustic and electromagnetic scattering data, providing a rigorous characterization and numerical validation.

Contribution

It introduces a novel factorization approach tailored for anisotropic media with defects, including voids, with theoretical analysis and numerical demonstrations.

Findings

Successful reconstruction of defective regions from far field data.

Method applicable to both acoustic and electromagnetic scattering.

Numerical examples confirm the feasibility of the approach.

Abstract

In this paper we consider the inverse acoustic scattering (in \mathbb{R}^3) or electromagnetic scattering (in \mathbb{R}^2, for the scalar TE-polarization case) problem of reconstructing possibly multiple defective penetrable regions in a known anisotropic material of compact support. We develop the factorization method for a non-absorbing anisotropic background media containing penetrable defects. In particular, under appropriate assumptions on the anisotropic material properties of the media we develop a rigorous characterization for the support of the defective regions from the given far field measurements. Finally we present some numerical examples in the two dimensional case to demonstrate the feasibility of our reconstruction method including examples for the case when the defects are voids (i.e. subregions with refractive index the same as the background outside the inhomogeneous hosting media).