Optimized Numerical Evaluation of Singular and Near-Singular Potential Integrals Involving Junction Basis Functions

In analyzing conducting bodies composed of surfaces connected to wires via a method of moments discretization of the electric field integral equation, junction basis functions are defined at connection points between wires and surfaces to correctly capture the physics of the current flux in the vicinity of the junction. In evaluating the associated self-term vector potential surface integrals, two singularities are present: one is related to the Green's function, and the other is due to the 1/ρ behavior of the junction basis function that models the current near a junction. Here we present a simple and efficient numerical procedure for evaluating singular and near-singular source vector potential integrals involving junction basis functions. The approach is based on a double transformation that cancels both singularities and also overcomes some limitations of singularity subtraction methods. The proposed scheme is then optimized to obtain at least four correct digits in the evaluation of these integrals. Essentially arbitrary accuracy is achievable by suitably increasing the quadrature order.