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The properties of hypersingular integrals, which arise when the gradient of con­ ventional boundary integrals is taken, are discussed. Interpretation in terms of Hadamard finite-part integrals, even for integrals in three dimensions, is given, and this concept is compared with the Cauchy Principal Value, which by itself is insuffi­ cient to render meaning to the hypersingular integrals. It is shown that the finite-part integrals may be avoided, if desired, by conversion to regular line and surface inte­ grals through a novel use of Stokes' theorem. Motivation for this work is given in the context of scattering of time-harmonic waves by cracks. Static crack analysis of linear elastic fracture mechanics is included as an important special case in the zerofrequency limit. A numerical example is given for the problem of acoustic scattering by a rigid screen in three spatial dimensions.

The boundary element method applied to static and dynamic crack problems using hypersingular boundary integral equations