Progress with numerical integration of the near-singular Green function gradient on general triangle domains

Curvilinear, higher-order, triangular elements are often used in the Method of Moments (MoM). In such cases quadrature schemes based on near-singularity cancellation transformations have shown great promise. This paper focuses on the field evaluation integral involving the scalar Green function gradient kernel grad(1/R). Schemes based on splitting into three sub-triangles, followed by near-singularity cancellation transformations are compared. The three-subdomain methods offer easy control of accuracy. The results suggest that an enhanced version of the existing Augmented-Duffy-R1-Linear scheme is more efficient than the other schemes available in the literature at present.