Author(s)

L.J. Gray & L.L. Marine

Abstract

Hypersingular integrals at a corner L.J. Gray, L.L. Marine Mathematical Sciences Section, Oak Ridge C/6V1 ABSTRACT For a smooth boundary, hypersingular integrals can be defined as a limit from the interior, the approach direction being taken, for convenience, normal to the surface. A limit definition is also valid at a boundary corner, provided a con- sistent approach direction is employed for all singular integrals. The analytical formulas for these integrals are more complicated than for a smooth surface, but are easily obtained using symbolic computation. These techniques will be em- ployed to accurately solve the '(.-shaped domain' potential problem considered in the text by Jaswon and Symm. As demonstrated therein, standard boundary el- ement methods applied to this problem yield inaccurate solutions at the corners. INTRODUCTION For many applications, a boundary integral analysis can be considerably im- proved

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