Singularity subtraction integral formulae for surface integral equations with RWG, rooftop and hybrid basis functions

Abstract

Numerical solution of electromagnetic scattering problems by the surface integral methods leads to numerical integration of singular integrals in the Method of Moments. The heavy numerical cost of a straightforward numerical treatment of these integrals can be avoided by a more efficient and accurate approach based on the singularity subtraction method. In the literature the information of the closed form integral formulae required by the singularity subtraction method is quite fragmented. In this paper we give a uniform presentation of the singularity subtraction method for planar surface elements with RWG, n̂×RWG, rooftop, and n̂×rooftop basis functions, the latter three cases being novel applications. We also discuss the hybrid use of these functions. The singularity subtraction formulas are derived recursively and can be used to subtract more than one term in the Taylor series of the Green's function.