Numerical Integration Scheme for the Near-Singular Green Function Gradient on General Triangles

A new near-singularity cancellation transformation quadrature scheme for triangle domains is presented. It is tailored to the Green function gradient kernel (static and dynamic) multiplied with higher-order weighting functions on curvilinear triangles. The transformation is analytically invertible. Attention is paid to ensuring accuracy in both tangential and normal components. Such integrals must be routinely evaluated in modern method of moments (MoM) implementations. The scheme follows the standard three subtriangle splitting approach of which the benefits are single-parameter accuracy control, a geometry-independent total number of quadrature points and implementation simplicity. Extensive numerical results show superior efficiency and reliability to existing three-subdomain schemes. Consistent, dependable error convergence is demonstrated, with very low variation in accuracy for fixed quadrature order and singularity height. The scheme is suitable for practical use by MoM developers.