Colóquio 

27/09/2007, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Rainer Kress, University of Gottingen

Numerical Methods in Inverse Obstacle Scattering

For the approximate solution of the inverse obstacle scattering problem to reconstruct the boundary of an impenetrable obstacle from the knowledge of the far field pattern for the scattering of time-harmonic acoustic waves, roughly speaking, one can distinguish three groups of methods. Iterative methods interpret the inverse obstacle scattering problem as a nonlinear ill-posed operator equation and apply iterative schemes such as regularized Newton methods or Landweber iterations for its solution. Decomposition methods, in principle, separate the inverse problem into an ill-posed linear problem to reconstruct the scattered wave from its far field pattern and the subsequent determination of the boundary of the scatterer from the boundary condition. Finally, the third group consists of the more recently developed sampling and probe methods. In principle, these methods are based on criteria in terms of an indicator function that decides whether a point lies inside or outside the scatterer. The colloquium will give a survey by describing one or two representatives of each group including a discussion on the various advantages and disadvantages.