A point source method for inverse acoustic and electromagnetic obstacle scattering problems

Abstract

We present the mathematical foundation for a point-source method to solve some inverse acoustic and electromagnetic obstacle scattering problems in three dimensions. We investigate the inverse acoustic scattering problem by a sound-soft and a sound-hard scatterer and the inverse electromagnetic scattering problem by a perfect conductor. Two independent approaches to the method are presented which reflect its strong relation to basic properties of obstacle scattering problems. 1 Introduction. For numerous applications in medicine, geophysics and material science inverse acoustic and electromagnetic scattering problems are of great importance. Since many problems in these areas are not amenable to high or low frequency approximations one has to work with frequencies in the resonance region. This paper is concerned with the development of a point-source method (PSM) for the solution of some inverse acoustic and electromagnetic obstacle scattering problems in three dimensions. Point-sourc...