Discretization error due to the identity operator in surface integral equations

Abstract

We consider the accuracy of surface integral equations for the solution of scattering and radiation problems in electromagnetics. In numerical solutions, second-kind integral equations involving well-tested identity operators are preferable for efficiency, because they produce diagonally-dominant matrix equations that can be solved easily with iterative methods. However, the existence of the well-tested identity operators leads to inaccurate results, especially when the equations are discretized with low-order basis functions, such as the Rao-Wilton-Glisson functions. By performing a computational experiment based on the nonradiating property of the tangential incident fields on arbitrary surfaces, we show that the discretization error of the identity operator is a major error source that contaminates the accuracy of the second-kind integral equations significantly.