Abstract
On employing isoparametric, piecewise linear shape functions over a flat triangular domain, exact
expressions are derived for all surface potentials involved in the numerical solution of three-dimensional
singular and hyper-singular boundary integral equations of potential theory. These formulae, which are
valid for an arbitrary source point in space, are represented as analytic expressions over the edges of
the integration triangle. They can be used to solve integral equations defined on polygonal boundaries
via the collocation method or may be utilized as analytic expressions for the inner integrals in the
Galerkin technique. Also, the constant element approximation can be directly obtained with no extra
effort. Sample problems solved by the collocation boundary element method for the Laplace equation
are included to validate the proposed formulae.