Comparison of near-singularity cancellation quadrature schemes for curvilinear triangle domains

In the method of moments (MoM) a routine requirement is the integration of near-singular kernels over triangle domains. Increasingly, higher-order basis functions and curvilinear mesh elements are used. Near-singularity cancellation quadrature is an attractive approach for evaluating such integrals. This paper investigates the effect of curvi-linearity upon the accuracy of these quadrature schemes. Comparative results for flat and curvilinear domains with different orders of weighting functions are presented. The kernels 1/R and grad(1/R) are considered. It is found that switching to a curved domain has a similar effect as including a higher-order weighting function. Conclusions regarding the most efficient schemes are also drawn.