Efficient Evaluation of Weakly Singular Integrals Arising From Electromagnetic Surface 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 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 $1/R$ weak singularity in the integral kernel, where $R$ is the distance between an observation point and a source point. The weakly singular integral 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 integral by using a local polar coordinate system. The approach can automatically cancel the singularity and reduce the integral to a one-fold numerical integration by deriving a closed-form expression for the integral over the polar coordinate. Numerical examples are presented to demonstrate the effectiveness of the approach.