Numerical Solution of Obstacle Scattering Problems
  Some novel numerical approaches to solving direct and inverse obstacle scattering problems (IOSP) are presented. Scattering by finite obstacles and by periodic structures is considered. The emphasis for solving direct scattering problem is on the Modified Rayleigh Conjecture (MRC) method, recently introduced and tested by the authors. This method is used numerically in scattering by finite obstacles and by periodic structures. Numerical results it produces are very encouraging. The support function method (SFM) for solving the IOSP is described and tested in some examples. Analysis of the various versions of linear sampling methods for solving IOSP is given and the limitations of these methods are described. 
Alexander G. Ramm, Semion Gutman