HYPERSINGULAR AND FINITE-PART INTEGRALS IN THE BOUNDARY-ELEMENT METHOD

A new definition of the Hadamard finite part (HFP) of hypersingular in tegrals is proposed in this paper. This definition does not involve a limiting process. It is completely general and is valid for one as wel l as higher dimensional integrals, on closed as well as on open surfac es. It reduces, respectively, to the Cauchy principal value (CPV) and Riemann integral, respectively, for the special cases of strongly sing ular and weakly singular integrands. Of course, suitable symmetric exc lusion zones must be chosen to realize CPV integrals. Starting with th is new definition of the HFP of certain hypersingular boundary integra l equations (HBIE) that arise in potential theory and in wave scatteri ng, a regularization method is carried out in order to express the hyp ersingular integrals in terms of ones that are, at most, weakly singul ar. The regularized versions are completely consistent with those avai lable in the recent literature where a different definition of the HFP was employed.