Abstract
An accurate and efficient semi-analytic integration technique is developed for three-dimensional hypersingular
boundary integral equations of potential theory. Investigated in the context of a Galerkin approach, surface
integrals are defined as limits to the boundary and linear surface elements are employed to approximate the
geometry and field variables on the boundary. In the inner integration procedure, all
singular and non-singular integrals over a triangular boundary element are expressed exactly as analytic formulae
over the edges of the integration triangle. In the outer integration scheme, closed-form expressions are obtained
for the coincident case, wherein the divergent terms are identified explicitly and are shown to cancel with
corresponding terms from the edge-adjacent case. The remaining surface integrals, containing only
weak singularities, are carried out successfully by use of standard numerical cubatures.
Sample problems are included to illustrate the performance and validity of the proposed algorithm.