Direct evaluation of hypersingular Galerkin surface integrals II

Abstract

Direct boundary limit algorithms for evaluating hypersingular Galerkin surface integrals have been successful in identifying and removing the divergent terms, leaving finite integrals to be evaluated. This paper is concerned with the numerical computation of these multi-dimensional integrals. The integrands contain a weakly singular logarithmic term that is difficult to evaluate directly using standard numerical techniques. Herein it is shown that analytic integration of these weakly singular terms can be accomlished by suitably re-ordering the parameter integrals. In addition to improved accuracy, this process also reduces the dimension of the numerical quadrature, and hence improves efficiency.