A Singularity Cancellation Technique for Weakly Singular Integrals on Higher Order Surface Descriptions

Accurate integration of singular and near-singular functions is critical to the accuracy of the method of moments solution to surface integral equations. While this problem has been widely addressed for flat geometries, its extensions to higher order surface descriptions have been limited. This letter provides a systematic prescription for the application of the rules for weakly singular integrals on higher order surfaces. Here, we present implementation details and several demonstrative results that compare the accuracy and convergence of the integration rules.

I. Introduction

Method of moments (MoM) solution to integral equations involves integration of a singular kernel on a surface. The computation of this integral needs to be carefully addressed in order to ensure accurate solutions. This has been a recognized concern for several years, and a significant quantity of research has been devoted to the development of methods to handle singularities [1]–[8], [19], mostly on flat triangular domains. Relatively recent work demonstrating the advantages of higher order surface descriptions [9]–[11] necessitates the extension of these singular integration rules for higher order surfaces, and this will be the focus of this communication.