ON THE VALIDITY OF CONFORMING BEM ALGORITHMS FOR HYPERSINGULAR BOUNDARY INTEGRAL-EQUATIONS

The widely held notion that the use of standard conforming isoparametr ic boundary elements may not be used in the solution of hypersingular integral equations is investigated. It is demonstrated that for points on the boundary where the underlying field is C-1,C-alpha continuous, a class of rigorous nonsingular conforming BEM algorithms may be appl ied. The justification for this class of algorithms is interpreted in terms of some recent criticism. It is shown that the numerical integra tion in these conforming BEM algorithms using relaxed regularization r epresents a finite approximation to the standard two-sided Hadamard fi nite part interpretation of hypersingular integrals. It is also shown that the integration schemes in this class of algorithms are not based upon one-sided finite part interpretations. As a result, the attendan t ambiguities associated with the incorrect use of the one-sided inter pretations in boundary integral equations pose no problem for this cla ss of algorithms. Additionally, the distinction is made between the an alytic discontinuities in the field which place limitations on the app licability of the conforming BEM and the discontinuities resulting fro m the use of piece-wise C-1,C-alpha interpolations.