A numerical regularization of EFIE for printed structures

The electric field integral equation (EFIE) used in the analysis of printed structures is a strongly singular, first-kind Fredholm equation. Its regularization is the transformation into a second-kind one with smooth kernel, with strongly improved numerical properties, via inversion of the singular part. For layered media, this technique has been so far confined to two-dimensional problems in which the inversion can be carried out in closed form. Here, the regularization issue for a general structure will be addressed via a novel approach with numerically-based inversion of the singular part of the operator. In the general case, it is shown that a splitting of the solution into two parts is required, which however improves the efficiency of the solution. As a byproduct, it will also be shown that practical convergence of the solution to the EFIE is assured by the strong singularity of the kernel, provided this is correctly kept in the solution process.