On the testing of the identity operator and the accuracy improvement of the second-kind SIEs

Abstract

Surface integral equations (SIEs) are widely used in the numerical analysis of electromagnetic wave scattering and radiation problems. However, the second-kind Fredholm integral equations are always found to produce less accurate numerical solutions than their first-kind counterparts. Among the variety of error sources, the discretization error due to the identity operator contributes the most. When the low-order basis functions, such as the Rao-Wilton-Glisson (RWG) basis functions, are used to expand the unknown current densities, the Galerkin's testing introduces a significant error in the solution. In this paper, the Buffa-Christiansen (BC) functions are shown to be a better testing function than the RWG function in the context of the method of weighted residuals (MWR). By using the BC as the testing functions, the numerical error of the identity operator, as well as that of the second-kind integral equations, are suppressed dramatically. Several numerical examples are given to demonstrate the accuracy improvement in both perfect electric conductor and dielectric scattering cases.