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Reduction of volume-volume integrals arising in galerkin JM-VIE formulations to surface-surface integrals

The numerical evaluation of current-based volume integral equation formulations typically involves 6-D integrals with kernels that exhibit strongly singular or weakly singular behavior when observation points coincide with source points. We demonstrate that these integrals can be reduced to 4-D integrals with smoother kernels that are amenable to numerical evaluation by means of well-established numerical schemes originally developed for surface integral equation formulations.