Convergence of the MPIE Galerkin MoM Thin Wire Formulation

Convergence studies of the Method of Moments solution of thin wires have long been handicapped by the issue of conditional convergence: when the segment length approaches the wire radius, the approximations typically made result in exponentially diverging solutions. In this communication, it is shown that it is the approximation of the singularity which is the main cause of this problem. Using the mixed potential integral equation, paralleling the classic RWG formulation for surfaces, the formulation in this communication approximates the surface (as opposed to equivalent filamentary) current, and applies Galerkin testing on the wire surface. The use of contemporary singularity-canceling integral transforms for highly efficient and accurate quadrature is demonstrated. Results are presented for typical thin-wire dipoles for both radiation and scattering problems. It is shown that with a rigorous treatment of the singularity, a far more comprehensive convergence study may be undertaken than previously demonstrated. Furthermore, the results shown justify the many years of successful use in practice of simple source models with modest mesh requirements.