The factorization method for the scattering by a mixed inhomogeneous medium

Abstract

We use the classical factorization method proposed firstly by Kirsch to reconstruct the support of the mixed inhomogeneous medium associated with complex valued refractive indexes and different transmission boundary conditions. We will show that for well-chosen inhomogeneous backgrounds, one obtains a necessary and sufficient condition characterizing the support of the medium via the eigensystem of a self-adjoint operator, which is related to the far field operator. Moreover, for completeness of our problem, the variational method is applied to solve the direct scattering problem. And, we present a variant of numerical examples in 2D to verify the effectiveness and robustness of the proposed inverse algorithms.