A novel numerical method for evaluation of hypersingular integrals in electromagnetics

Abstract

In this study we develop a numerical method for evaluation of hypersingular surface integrals, which arise in the solution of electric field integral equation (EFIE) via Nystrom method. Due to the divergent contribution of an infinitesimal area around the singular point, hypersingular integrals are told to be numerically intractable and analytical methods are employed for evaluation of these integrals. In this study we interpret hypersingular integrals as the second order derivative of weakly singular integrals, which can be efficiently evaluated using quadrature rules. By evaluating the derivative of weakly singular integrals numerically, we have shown that hypersingular integrals can accurately be evaluated using the proposed method. We have solved a scattering problem via Nystrom method to confirm the validity of the method.