On status of main singularities in 3D scattering problems

As it is known, the procedure of solution of scattering problems by the method of auxiliary sources (MAS) needs preliminary considerations of various problems: (a) choice of auxiliary surface; (b) choice of type of auxiliary sources (AS), these sources can be fundamental or other singular solutions of the wave equation; and (c) choice of the way of determination of unknown auxiliary sources. Correct solution of these problems can radically influence the efficiency of the MAS. These problems are tightly bound with the problem of localization of main singularities of scattered field (SFMS). In the current work a new procedure of localization of SFMS is presented. The procedure is valid for piece-wise analytical 3D surfaces. It is shown, that using method of collocations, it is necessary to consider the functional dependence of the positions of collocation points on the positions and type of SFMS