Spurious oscillations in a combined Method-of-Auxiliary-Sources/Extended-Integral-Equation solution to a simple scattering problem

Recent studies of the Method of Auxiliary Sources (MAS) solutions to a simple scattering problem have shown that it is possible to have convergence of the field, which is the finally desired quantity, together with divergence of the MAS currents, which are intermediate quantities. Another recent study has demonstrated that no similar phenomenon occurs when the computational method is a certain discretization of the Extended Integral Equation (EIE); this integral equation is due to Peter C. Waterman. The purpose of the present paper is to extend these findings to a combined MAS/EIE method that can be viewed as one possible 2-D implementation of what is usually called the Null-Field Method with Discrete Sources (NFMDS). We find that, despite the convergence of the field, divergence of currents-manifesting itself as spurious oscillations-can occur within this combined method under certain conditions. We point out extensions to more complicated scattering problems, and discuss why the phenomenon under study is undesirable in practice.

► We analyze the combined MAS/EIE solution of a simple problem. ► Under certain conditions, divergence of the auxiliary currents can occur. ► When divergence occurs, the combined MAS/EIE method still gives the correct fields. ► We discuss why the divergence is undesirable in practice.