The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on October 6, 2015 at 14:00 in Room 478 of IMI.

A talk on:

The Factorization Method for Inverse Scattering Problems

will be delivered by Prof. Andreas Kirsch, Karlsruhe Institute of Technology, Germany.

Everybody is invited.

Abstract. We consider the inverse scattering problem to determine the shape of a sound-soft obstacle from the knowledge of the scattered fields corresponding to time-harmonic acoustic plane waves. We first formulate the direct and inverse scattering problems rigorously and report on classical approaches for solving the inverse problem numerically. Then we present a non-iterative approach which belongs to a class of sampling methods. We construct a binary criterion to determine whether or not a given point belongs to the scatterer. This method is mathematically rigorous and elegant and provides an explicit formula for the characteristic function of the unknown scatterer. One of the advantages of this Factorization Method is that it does not need to know the kind of boundary condition in advance or the number of components of the scatterer.