Numerical Singular Integral Methods for Computational Electromagnetics

Efficient Numerical Singular Integral (NSI) methods have been developed for both 1D and 2D electromagnetics problems, in both the Cartesian and polar coordinates. Through a special type of integration by parts, rigorous mathematics derivation has been performed to decompose the original singular integrals into sum of non-singular integrals that can be evaluated numerically. It can be shown that it is more convenient to evaluate the line-type singularity in the Cartesian coordinate; while it is better to evaluate the point-type singularity in the polar coordinate. Also, numerical schemes to find the order of singularity has been presented. Finally, to validate the 2D numerical singular integral methods, the electromagnetic scattering problem of a 2D reflecting ellipse antenna has been simulated through the Ping-Pong algorithm developed by the authors.