Reduction of Singular Surface Integrals to Nonsingular Line Integrals in Integral Equations for Planar Geometries

Abstract

A novel procedure is presented for the evaluation of matrix elements of the tensor Green function with Rao–Wilton–Glisson basis functions appearing in surface integral equations in electromagnetics. The procedure, at this point applicable to planar geometries, or geometries composed of parallel planar sheets, reduces 4-D surface integrals with singular integrands to line integrals over triangle edges with regular integrands. The main advantage of the derived expressions is that they offer simplicity and easily controllable accuracy achieved at a computational cost significantly lower than for previously considered techniques, in particular the conventional singularity subtraction method.