In this paper, we characterize the logarithmic singularities arising in the method of moments from the Green’s function in integrals over the test domain, and we use two approaches for designing geometrically symmetric quadrature rules to integrate these singular integrands. These rules exhibit better convergence properties than quadrature rules for polynomials and, in general, lead to better accuracy with a lower number of quadrature points. We demonstrate their effectiveness for several examples encountered in both the scalar and vector potentials of the electric-field integral equation (singular, near-singular, and far interactions) as compared to the commonly employed polynomial scheme and the double Ma–Rokhlin–Wandzura (DMRW) rules, whose sample points are located asymmetrically within triangles.

在本文中，我们描述了格林函数在测试域上的矩函数方法中产生的对数奇异性，并使用两种方法设计几何对称正交规则来集成这些奇异被积体。与多项式的正交规则相比，这些规则具有更好的收敛性，并且通常，使用较少的正交点可导致更高的精度。与常用的多项式方案和双重Ma–Rokhlin–Wandzura（（）相比，我们在电场积分方程的标量和矢量势（奇异，近奇和远相互作用）中遇到的几个示例中证明了它们的有效性。 DMRW）规则，其采样点不对称地位于三角形内。