On the efficient evaluation of hyper-singular integrals in Galerkin surface integral equation formulations via the direct evaluation method

In this paper, the direct evaluation method is outlined for the computation of the hypersingular integrals arising in Galerkin surface integral equation formulations. The key feature of the proposed scheme lies on the appropriate regularization of the singular integrand together with the reduction of the dimensionality of the original integral from 4-D to 2-D. The procedure presented herein succeed in providing numerical results of unmatched accuracy (close to the machine precision) and efficiency, thus, improving substantially the accuracy of the impedance matrix elements in field integral equation formulations as well as reducing the overall filling time.