A combination of shape and conductivity function reconstruction methods for an inverse boundary value problem

Abstract

In this paper, an integral equation based method for the reconstruction of two-dimensional shape of a buried sound-soft obstacle and a real valued conductivity function defined over the exterior cylinder is presented. The direct problem considered here is to compute the scattered near/far field, for given shapes, wave numbers and conductivity function in the case of a single time-harmonic acoustic plane wave insonification. The aim of the inverse problem is to find the shape of the buried sound-soft obstacle as well as the conductivity function from the knowledge of the near/far field for given shape of the homogenous outer cylinder. In order to avoid an inverse crime different Potential approaches are used to derive a system of boundary integral equations and they are evaluated by using Nyström method numerically. To get stable solutions for the first kind of integral equations Tikhonov regularization is applied. Finally, numerical results are presented out to test the applicability and the effectiveness of the method.