A Reverse Operation Self-Consistent Evaluation Approach for Singular Integrals in the SIE Analysis of PEC Targets

Discussed herein is a novel approach entitled reverse operation self-consistent evaluation (ROSE). Specifically, we applied ROSE for the treatment of weak-singular and hypersingular kernels in surface integral equations (SIEs) for the computation of electromagnetic (EM) scattering from perfect electrical conductors (PECs). Different from the existing forward methods, ROSE is based on reverse operations. The singular entries are not evaluated directly by analytical or numerical evaluation; instead, they are introduced as unknowns and are solved algebraically. For EM scattering from PEC, SIEs can be set up by using the Stratton-Chu representation formula. An auxiliary problem with the same meshed boundary is then formulated, of which any plane waves are the self-consistent solutions. It is shown that by applying a consistent discretization, the matrix of the auxiliary problem can be made identical with the original one. As a consequence, these self-consistent solutions can be utilized to solve the singular entries of the original system. Explicitly, a set of plane waves are interpolated using the appropriate basis functions. Subsequently, the corresponding coefficient vectors are utilized to construct small linear systems to solve the troublesome singular entries in the underlying matrix. The proposed ROSE approach is applicable to different singular kernels as well as different discretization schemes. In this paper, we restrict our discussion to the weak-singular and hypersingular kernels using, respectively, div-conformal Rao-Wilton-Glisson basis functions and nonconformal piecewise constant vector basis functions. Accelerated by the multilevel fast multipole algorithm, the proposed method is applicable for real-life applications.