The inverse transmission eigenvalue problem for a discontinuous refractive index
In this talk we will present results concerning the recovery of the index of refraction for the interior transmission problem from a set of transmission eigenvalues. We define the inverse spectral problem for a spherically symmetric medium with a refractive index with a finite number of discontinuities. Afterwards, we present theoretical results concerning conditions in order to have uniqueness of location of the discontinuities and preliminary results for the inverse problem. Next we propose a numerical Newton based method for the reconstruction of a discontinuous refractive index in domains with smooth boundary from a finite number of real and complex eigenvalues and show numerical results demonstrating the applicability of the method.