A Practical Implementation and Comparative Assessment of the Radial-Angular-Transform Singularity Cancellation Method

A practical numerical integration approach is proposed for the radial-angular-transform singularity cancellation (SC) method such that all singular and near-singular integrals encountered in the method-of-moments (MOM) solution of integral equations are evaluated to arbitrary pre-specified error levels. In the proposed approach, the transformed MOM integrals are evaluated using the progressive Gauss–Patterson quadrature rules that provide on-the-fly error estimates; these error estimates are used to automate the choice of quadrature rules in the SC method whose performance strongly varies from one impedance matrix entry to another. This progressive numerical integration approach is carefully compared to a naïve implementation of the SC method that uses static quadrature rules as well as to the more common singularity extraction (SE) method. Specifically, the SC and SE methods are applied to the classical solution of the frequency-domain electric field integral equation using RWG basis functions and several scattering problems are solved in the low- and high-frequency regimes of analysis. Numerical results show that although the proposed approach improves the efficiency of the SC method significantly, the SE method, especially if high-order asymptotic forms of Green functions can be extracted, remains the most efficient alternative when applicable.