An analytical method of auxiliary sources solution for plane wave scattering by impedance cylinders - A reference solution for the numerical method of auxiliary sources

摘要

To facilitate the validation of the numerical Method of Auxiliary Sources an analytical Method of Auxiliary Sources solution is derived in this paper. The analytical solution is valid for transverse magnetic, and electric, plane wave scattering by circular impedance cylinders, and it is derived by transformation of the exact eigenfunction series solution. The transformation employs the Hankel function wave transformation to express the eigenfunction series of higher-order Hankel functions, with their singularities at the coordinate system origin, as a superposition of zero-order Hankel functions with their singularities at different positions away from the origin. The transformation necessitates a truncation of the wave transformation but the inaccuracy introduced hereby is shown to be negligible. The analytical Method of Auxiliary Sources solution is employed as a reference to investigate the accuracy of the numerical Method of Auxiliary Sources for a range of scattering configurations.