HYPERSINGULAR INTEGRALS AT A CORNER

For a smooth boundary, hypersingular integrals can be defined as a lim it from the interior, the approach direction being taken, for convenie nce, normal to the surface. At a boundary corner, the limit process, w ith a necessarily non-normal approach direction, provides a valid defi nition of the hypersingular equation, as long as the same direction is employed for all integrations. The terms which are potentially singul ar in the limit are shown to cancel, provided the function approximati ons at the corner are consistent. The analytical formulas for the sing ular integrals are more complicated than for a smooth surface, but are easily obtained using symbolic computation. These techniques have bee n employed to accurately solve the 'L-shaped domain' potential problem considered by Jaswon and Symm (Integral Equation Methods in Potential Theory and Elastostatics, Academic Press, New York, USA, 1977).