A reconstruction method based on topological derivatives for an inverse problem modeled by the Helmholtz equation

Abstract

This paper deals with an inverse potential problem whose forward problem is governed by the Helmholtz equation. The inverse problem consists in the reconstruction of a set of anomalies embedded into a fluid medium with the help of partial measurements of the associated potential. We rewrite the inverse problem as a topology optimization problem which allows us to solve it by using the concept of topological derivatives. The resulting algorithm is able to reconstruct the anomalies in one step and is independent of any initial guess. A numerical example is presented to show the effectiveness of our reconstruction method.