On the Treatment of Strongly Singular Integrals Over Flat Triangular Domains

摘要

Conventional Method of Moment (MoM) employs divergence-conforming basis functions to expand unknown current densities so that the treatment of higher-order singular integrals can be facilitated. Compared with MoM, the Nyström method interpolates unknown functions with polynomials of arbitrary orders, which not only decreases the computational cost of matrix entries, but also enables the use of nonconforming grids. However, the Nyström method must treat the higher-order singular integrals related to dyadic Green's function. The dyadic Green's function gives rise to strongly singular integrals which are challenging to handle. This paper presents new closed-form formulas for calculating strongly singular integrals. A numerical example is used to demonstrate the approach and good result has been observed.