All-analytical evaluation of the singular integrals involved in the Method of Moments

TL;DR

This paper introduces an all-analytical approach for evaluating singular integrals in the Method of Moments, applicable to flat polygonal basis and testing functions, improving accuracy and efficiency in surface integral equation methods.

Contribution

It presents a novel all-analytical formula for singular integrals in EFIE and MFIE, applicable to any flat polygonal basis and testing functions of any order.

Findings

Competitive with existing techniques in accuracy and speed

Applicable to any flat polygonal basis and testing functions of any order

Enhances the precision of singular integral evaluations in SIE methods

Abstract

Surface Integral Equation (SIE) methods routinely require the integration of the singular Green's function or its gradient over Basis Functions (BF) and Testing Functions (TF). Many techniques have been described in the literature for the fast and accurate computation of these integrals for TF that is located close to the BF. In this paper, we propose an all-analytical formula for the singular part of the integral for both the Electric and Magnetic Field Integral Equations (EFIE and MFIE). The method works for any flat polygonal BF and TF of any order, and proves to be competitive with existing techniques.