A single domain approach to weak near-singularity cancellation quadrature on triangle domains

Abstract

In electromagnetic field modelling, the method of moments (MoM) is regularly used to solve surface currents. Recently, much progress has been made with numerical integration methods for the evaluation of the singular and near-singular surface integrals occurring in the MoM, especially in the context of using curved surface elements (curvilinear) with higher-order basis functions. The focus here is on the near-singular scalar Green's function kernel, when integrated over a triangle domain. This is a weak near-singularity. A first version of a new near-singularity cancellation quadrature rule is presented, which is constructed by applying a single near-singularity cancellation transformation to the whole domain, without splitting it into three sub-triangle domains as is typically done in other methods. The aim is to reduce the number of required quadrature points for a given accuracy. Promising preliminary results are shown, but there are various aspects that require further investigation and optimization.