Diffraction problem solution based on use of spherical-wave sources

We consider an external problem of diffraction by compact bodies, for which the region containing a set of singularities of the analytic continuation of the wave field is known. The approach to solution of this problem is based on representing the scattered field as series of spherical waves divergent from several centers with the amplitudes determined from the boundary condition by solving the inverse problem. The condition indicating the minimum number of radiation centers and their optimal location inside the scatterer is obtained. The results of numerical simulation are reported.