Accuracy analysis and optimization of the method of auxiliary sources (MAS) applied to TE scattering by a perfectly conducting circular cylinder

The purpose of this paper is a rigorous accuracy analysis of the method of auxiliary sources (MAS), when the latter is applied to electromagnetic scattering problems. The scattering geometry involves a perfectly conducting, infinite, circular cylinder, illuminated by a transverse electric (TE) plane wave. The MAS square matrix is shown to be analytically invertible, leading to exact mathematical expressions for the discretization error and the condition number of the pertinent linear algebraic system. An asymptotic estimate of the condition number for large scatterers is also derived. Among several important results of the analysis, the fundamental MAS question regarding the optimal location of the auxiliary sources is investigated and resolved for this particular geometry.