Error analysis of singularity cancellation quadrature on curvilinear triangles

Abstract

In computational electromagnetics, when using the method of moments (MoM) to solve surface integral equations, numerical integration of near-singularities is required. Here, a brief overview of a theoretical error analysis for the recently proposed Arcsinh transformation-based quadrature scheme, generalized to curvilinear triangle domains, is given. Gaussian product rule quadrature is also considered in this context. Accurate error prediction is demonstrated. Insights gained into the error mechanisms of the Arcsinh scheme enable one to use it with confidence where applicable. Such situations are mild near-singularities and especially, extreme near-singularities. These occur within the MoM.