The Numerical Solution of the Three-Dimensional Inverse Scattering Problem for Time Harmonic Acoustic Waves

Abstract

The inverse scattering problem under consideration is to determine the shape of an acoustically soft obstacle in $\mathbb{R}^3 $ from a knowledge of the time harmonic incident wave and the far field pattern of the scattered wave. It is assumed that the frequency is in the resonance region, i.e. high frequency asymptotic methods are not available. A method for solving this problem is presented which is based on the theory of Herglotz wave functions and avoids the use of integral equations. Numerical examples are given showing the practicality of this approach.