The Method of Auxiliary Sources (MAS) — Solution of Propagation, Diffraction and Inverse Problems Using MAS

Abstract

Mathematical justification of the MAS was done by Georgian mathematicians (Kupradze [1], Vekua [2]). There is also the number of works which authors, probably independently, offered such representation of scattered fields [3–9]. In [1,2] it is proved that for arbitrary closed auxiliary surface inside area D the solution tends to the true one with the increasing of the number of auxiliary sources (AS). Some of the authors considered such approach only as a mathematical way of constructing the solutions of the physical problem and did not consider any physical meanings. During the solution of applied problems it has been shown that the basic difficulties arise unless all physical properties of the scattered field (SF) are taken into account in the algorithm and vice versa. Stability, and convergence depends on the correct choice of auxiliary parameters considering the physical meaning. So the modern algorithm of the MAS is developed as a numerical method for the solution of boundary problems of mathematical physics [10].