Direct and Inverse Scattering by 3D Rough Surfaces - Progress and Challenges
Roland Potthast

Abstract: We will discuss wave the problem of scattering by three dimensional rough surfaces. The mathematics of these problems as well as the algorithmical solution of direct and inverse problems and the numerical analysis of the algorithms provide sincere challenges since the methods developed for bounded objects cannot be directly translated to the setting of unbounded scatterers. We survey recent results on the direct and inverse problems by Burkard, Chandler-Wilde, Heinemeyer, Lindner and the speaker. For the multi-section method, we present a numerical scheme for which the convergence, both for the direct and the inverse scattering (using a multi-section Kirsch-Kress approach), can be shown. Finally, we will show recent theoretical and numerical results on a time-domain probe method for shape reconstruction for rough surfaces in acoustics.