Numerical evaluation of singular matrix elements in three dimensions (Maxwell equations)

In using the moment method to get approximate solutions of Maxwell's equations, the matrix elements are usually expressed as integrals involving a singular kernel. Numerical evaluation of the matrix requires special consideration where the singularity is of high order. The question addressed is how best to compute matrix elements in the presence of this strong singular term for a discrete system defined on a rectangular grid. A systematic way of approximating both the singular and the nonsingular integrals over rectangular volumetric cells is given. The singular integrals are regularized, using a cubic exclusion volume, and the exclusion volume integrals are approximated using polynomial expressions. Suggestions are made on how to treat the nonsingular integrals. The results can be applied to three-dimensional electromagnetic problems to determine the field in penetrable inhomogeneous bodies.<
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