NUMERICAL EVALUATION OF SINGULAR MATRIX-ELEMENTS IN 3 DIMENSIONS

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. Although the nature and treatment of the high-order singularity has been discussed extensively in the literature, an explicit prescription for the numerical evaluation of the matrix elements for a system analyzed in Cartesian coordinates is not generally available. In this paper, 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 inhomogenous bodies. In particular, the results are applicable to the modeling of nondestructive evaluation by the eddy current method.