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Evaluation of 6-D MoM Integrals by Application of the Divergence Theorem with Singularity Subtraction Acceleration

We propose to evaluate the double-volumetric integrals appearing in MoM formulations for volumetric integral equations by applying the divergence theorem to reduce both source and test integrals to surface integrals. Their integrands consist of the original kernel, basis, and test functions integrated twice radially in closed form. Implementing the surface integrals directly in the physical domain eliminates the restrictions to well-shaped elements. For faceted volumetric elements, the surface integrals reduce to the evaluation of interaction integrals between source and test face pairs. Triangular facets may be either integrated directly in barycentric coordinates or in a cylindrical coordinate system whose axis is the line of intersection of planes containing source and test face pairs. Further smoothing of the integrand is provided by first removing the static asymptotic form of the integrand from the integral, then restoring its contribution as a closed form integral whose removal accelerates convergence of the difference integral.