Scattering by a Zero-Thickness PEC Disk: A New Analytically Regularizing Procedure Based on Helmholtz Decomposition and Galerkin Method

The aim of this paper is the introduction of a new analytically regularizing procedure, based on Helmholtz decomposition and Galerkin method, successfully employed to analyze the electromagnetic scattering by zero-thickness perfectly electrically conducting circular disk. After expanding the fields in cylindrical harmonics, the problem is formulated as an electric field integral equation in the vector Hankel transform domain. Assuming as unknowns the surface curl-free and divergence-free contributions of the surface current density, a second-kind Fredholm infinite matrix-operator equation is obtained by means of Galerkin method with expansion functions reconstructing the expected physical behavior of the surface current density and with closed-form spectral domain counterparts, which form a complete set of orthogonal eigenfunctions of the most singular part of the integral operator. The coefficients of the scattering matrix are single improper integrals which can be quickly computed by means of analytical asymptotic acceleration technique. Comparisons with the literature have been provided in order to show the accuracy and efficiency of the presented technique.