Accurate Solution for Surface Integral Equations with Sharp-corner Objects Based on Nyström Scheme

The electromagnetic (EM) problems with conducting objects can be described by surface integral equations (SIEs). Traditionally, the SIEs are solved by the method of moments (MoM). As an alternative method, the Nystrom scheme is proposed, which does not require any basis and testing functions and does not require conforming meshes, leading to much convenience in numerical implementations. Although the Nyström scheme has been widely used to solve various EM problems, it seldom dealt with the problems with highly sharp-corner objects and we present a robust solution method in this paper. To deal with the singularity, the closed-form formulas have been derived for evaluating singular integrals in the Cauchy-principal-value (CPV) sense. Two numerical examples are presented to demonstrate the scheme and good results have been obtained.