Study of Convergence, Divergence, and Oscillations in Method-of-Auxiliary-Sources (MAS) and Extended-Integral-Equation (EIE) Solutions to a Simple Cavity Problem

The Method of Auxiliary Sources (MAS) is a well-known method of computational electromagnetics and physics. Previous studies of MAS solutions to exterior scattering problems have shown that it is possible to have convergence of the field, which is the final desired quantity, together with divergence of the MAS currents, which are intermediate quantities. Another study has demonstrated that no similar phenomenon occurs when the computational method is a certain discretization of the extended integral equation (EIE). The purpose of the present paper is to extend these findings to interior scattering problems (i.e., scattering within cavities) and to point out differences with exterior problems. We discuss why the aforementioned phenomenon is undesirable in practice. We also investigate the relevancy of the analytic continuation of the interior scattered field to both MAS and the EIE.