Accurate and efficient numerical integration of weakly singular integrals in Galerkin EFIE solutions

A Galerkin descretization of the electric field integral equation for perfectly conducting surfaces using Rao-Wilton-Glisson (1982) basis functions requires the numerical evaluation of integrals with singular kernels over triangular regions. These singularities have been traditionally handled by utilizing a "singularity extraction" procedure to produce a regular integral and an analytic function to replace the original singular integral. A new approach is presented here in which the four-dimensional (4-D) weakly singular integrals unique to the Galerkin Rao-Wilton-Glisson electric field integral equation solution for perfectly conducting surfaces are transformed into integrals with regular integrands. The transformations allow some of the integrations to be performed analytically, in some cases reducing the original 4-D integral into a 1-D numerical integration. The accuracy and convergence properties of the new method are demonstrated by evaluating the scalar potential function over a unit triangle.