A static eigenfunction approach to the regularization of EFIE for printed antennas

This paper deals with a novel approach for the transformation (regularization) of the first-kind Fredholm EFIE for printed structures into a second kind equation. The first-kind EFIE is recast into two coupled, smaller problems, that exhibit the same singular, static-related behavior, that makes possible the inversion of these singular parts. The inversion is done via a numerical determination of the eigensystem of the singular operators; the resulting two classes of "static" eigenfunctions appear to be an extension of the TM and TE modes of a waveguide, coupled by the edge singularities. Examples of application show that the regularized system in this basis has favorable convergence properties, that permit one to approximate the solution with a few terms (e.g. 4-5 on a resonant patch), that can be selected a priori via the analysis of frequency-independent terms.