On the analytic calculation of multiple integrals in electromagnetics

Making use of a powerful Gauss divergence theorem and a new Gauss bi-divergence theorem, we transform a high dimensional moment integral into a lower dimensional boundary integral. This allows in most pertinent cases to replace the original singular multiple integral by a reduced non-singular multiple integral, which can be evaluated by means of standard analytic or numerical quadrature techniques. Some important electromagnetic cases are treated to indicate the strength and versatility of the proposed method.