A novel approach for evaluating singular integrals in electromagnetic integral equations

Solving electromagnetic(EM) problems by integral equation methods relies on the accurate evaluation of singular integrals related to the Green´s function. In the widely-used Method of Moments (MoM) with the Rao-Wilton-Glisson (RWG) basis function for solving surface integral equations (SIEs), the gradient operator on the scalar Green´s function can be moved onto the basic function and testing function, resulting in a 1/R singularity in the integral kernel, where R is the distance between an observation point and a source point. The singular integrals can be evaluated with the well-known Duffy´s method, but it requires a two-fold numerical integration. In this work, we develop a novel approach to evaluate the singular integrals by using a local polar coordinate system. The approach can cancel the singularity and reduce the integrals to a one-fold numerical integration by deriving a closed-form expression for the integrals over the polar coordinate. Numerical examples are presented to demonstrate the effectiveness of the approach.