Numerical Evaluation of Strongly Near-Singular Integrals in High-Order Method of Moments

Abstract

A numerical evaluation approach for strongly near-singular integrals in the high-order method of moments (MoM) is presented in this article. The approach starts with a three-subtriangle division and the establishment of a local coordinate system for each subtriangle. A Duffy transformation is then introduced to transform the surface integral in the Cartesian system into a radial–angular form to mitigate the singularities in the y-direction. According to the pole-based asymptotic analysis of the truncation error, successive sinh transformations are subsequently applied to both inner and outer integrals to accelerate the error convergence of numerical integration. Finally, by introducing a projection surface, the proposed method is further extended to curvilinear elements and applied to the high-order MoM. Numerical results have demonstrated the accuracy and efficiency of the proposed method for strongly near-singular integrals and its applicability in high-order MoM for practical electromagnetic (EM) scattering problems.