Evaluation of near-singularity cancellation quadrature schemes for the Green function gradient on higher-order triangles

Efficient evaluation of near-singular surface integrals is important to the efficient implementation of the MoM. The focus here is on the Green function gradient kernel. A near-singularity cancellation quadrature scheme under present development (AD-R1-L-AS2) is compared to other three-subdomain splitting methods available in the literature. The main benefit of the simple three sub-triangle splitting approach is that it allows accuracy control via a single parameter. The effect of a flat versus curvilinear integration domain is investigated as well as the effect of switching between the static and dynamic versions of the Green function gradient. The paper shows that the AD-R1-L-AS2 scheme is suitable for the cases considered and that it performs better in the tests conducted, than the other schemes considered.