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Acceleration of Volume-Volume (6-D) Integrals for Numerical Evaluation by Double Application of the Divergence Theorem

In the present paper, we propose the application of the surface divergence theorem for the integration of double volumetric integrals for both source and test domain of the 6-D reaction integrals. The resulting 6-D volume integrals are expressed as two radial integrals plus two surface integrals over the source and observation domain boundaries. The radial integrations in the physical domain should be well-behaved and easily performed for arbitrary polyhedral domains. The method is numerically validated for static and dynamic kernels arising in the Electric Field Integral Equation (EFIE), i.e., for kernels with 1/R singularities, and linear basis functions.