Progress in developing custom cubature rules for computational electromagnetics

Computational electromagnetics often requires the creation of quadrature and cubature rules beyond those found in the literature. In many situations rules are required for the accurate evaluation of integrals containing singularities; examples include 1/R singularities and singularities in the basis functions used to represent current or charge density at sharp edges and corners. Techniques for synthesizing quadrature rules involve the solution of nonlinear systems of equations. This presentation will describe recent progress as well as some of the challenges encountered by the authors in multidimensional quadrature rule synthesis.