Regularization of EFIE for printed structures: a numerical approach

The electric field integral equation (EFIE) used in the analysis of printed structures is a strongly singular, first-kind Fredholm equation. Its regulation is the transformation into a second-kind one with a 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. Numerical results are presented for a printed dipole to illustrate the technique; they show that a highly sparse matrix is obtained, with highly peaked diagonals.