Convergence Analysis of the Currents and Fields Involved in the Method of Auxiliary Sources Applied to Scattering by PEC Cylinders

The method of auxiliary sources (MAS) is an established technique for the numerical solution of electromagnetic shielding and scattering problems exhibiting an increasing interest for the simulation of various electromagnetic compatibility (EMC) applications. In previous works, it was shown that for the problem of transverse magnetic illumination of a perfect electric conducting cylinder by an electric current filament, it is possible for large numbers N of auxiliary sources that the MAS currents diverge and oscillate, while the generated MAS field converges to the exact solution. In this article, we further analyze the convergence issues and oscillations encountered in the MAS by considering the transverse electric case due to excitation by a magnetic current filament. We demonstrate analytically that the convergence/divergence phenomena of the currents and fields also occur in this problem and then study the nature of this divergence in detail. In particular, we prove a large-N asymptotic formula for the divergent MAS currents, which captures accurately the important characteristics of the associated inherent oscillations. Numerical results for noncircular shapes are also presented. The discussed effects must be carefully taken into account in EMC simulations pertaining to cylindrical conductors.