Estimating Quadrature Errors in the EFIE-Based MoM Matrix, Due to Inner Integrals

The method of moments based on the electric-field integral equation is widely used for numerically solving induced surface currents on conducting structures. To set up the impedance matrix, weakly singular and near-singular inner-surface integrals must be evaluated. A leading numerical integration scheme for this purpose is Radial-Angular-R1-Sqrt (RA-R1-Sqrt), near and true singularity cancellation transformation quadrature. For outer integrals, standard Gauss-Legendre quadrature is used. A new and improved, closed-form, RA-R1-Sqrt quadrature error estimate is derived. It is then used for a priori matrix entry error estimation due to inner integral, near-singularity quadrature. Standard, Rao-Wilton-Glisson basis functions on flat triangle elements are considered.