A Novel Integration Method for Weak Singularity Arising in Two-Dimensional Scattering Problems

In this paper, we introduce a novel mechanical quadrature method for an efficient solution of weakly singular integral equations arising in two-dimensional electromagnetic scattering problems. This approach is based on and adapted from the recently proposed mechanical quadrature methods in [Extrapolation algorithms for solving mixed boundary integral equations of the Helmholtz equation by mechanical quadrature methods, SIAM J. Sci. Comput., vol. 31, 4115-4129, 2009]. We report experiments for solving TM-polarized induced currents and scattered fields to show its superiority to the classical method of moments when accuracy is a concern. Moreover, additional numerical experiments made with an extrapolation algorithm suggest that the accuracy of the present method can be further improved dramatically by means of the extrapolation algorithm to some extent.