Singularity Evaluation of the Straight-Wire Mixed-Potential Integral Equation in the Method of Moments Procedure

A rigorous treatment on the computation of the various integrals that arise in the method of moments (MoM) formulation of the straight-wire electric field integral equation is provided. For triangle basis functions along with delta function, pulse or triangle weights, particular attention is given to integrals whose integrands are weakly singular. A singularity extraction technique is employed that splits the integral under question into two parts: one that is numerically integrable and one that is analytically integrable. Closed-form approximations based on Taylor series techniques are also provided for the former. These approximations are very robust resulting in errors less than 0.1% when 2a/delta < 1; here is the length of a single MoM segment and is the wire radius. Results are compared with data from the literature to demonstrate the robustness of the presented approach for fat wires.