An accurate and robust approach for evaluating VIE impedance matrix elements using SWG basis functions

In this paper, we present an iterative, efficient and accurate method for calculating singularities of both order 1/R and order 1/R² involved in the MoM solution of VIE. In our method, a sufficient number of terms from Green´s functions are subtracted so that the remainder is at least once continuously differentiable so as to enable the standard Gaussian quadrature method to be applicable. Similar ideas have been applied for surface integration problems in previous articles, here it is a further extension. Compared to the usual singularity extraction method which only extracts one term, the present method could significantly improve the accuracy of singular integral calculations. Compact iterative formulas are also derived and given here so that arbitrary terms of singularities can be subtracted and calculated analytically, which greatly facilitates its numerical implementation in the MoM procedure and also extendable to integral equation fast solvers.