EVALUATION OF HYPERSINGULAR INTEGRALS IN THE BOUNDARY-ELEMENT METHOD BY COMPLEX VARIABLE TECHNIQUES

Strongly singular and hypersingular integrals that occur in many two d imensional applications of the boundary element method (e.g. potential theory and liner elasticity) can be treated in a unified manner by co mplex analysis. This paper presents an elegant approach for the evalua tion of such hypersingular integrals. The limit to the boundary method , where a source point is moved from tile inside (or outside) of a bod y to its boundary, is carried out using complex variables. The connect ion of this limit with the Hadamard Finite part of hypersingular integ rals and principal value integrals is established. Many examples are w orked out throughout the paper to illustrate the theory. Copyright (C) 1996 Published by Elsevier Science Ltd.