## Rainer Kress (University of Göttingen)

The inverse obstacle scattering problem under consideration consists of
the reconstruction of the boundary of an impenetrable obstacle from the
knowledge of the far field pattern for scattering of time-harmonic acoustic
waves. The so-called decomposition methods separate this inverse problem
into an ill-posed linear problem to reconstruct the scattered wave from its far
field pattern followed by a nonlinear problem that determinates the boundary
shape of the scatterer from the boundary condition. We present recent
modifications of a decomposition method due to Kirsch and K. (1987) that
combines it with elements of Newton type iterations for inverse scattering
problems and lead to considerable improvements of the reconstruction quality.
The mathematical foundation of the new methods that rely on boundary
integral equations will be discussed and numerical examples will be presented.