Evaluation of hypersingular integrals in the boundary element method by complex variable techniques

Strongly singular and hypersingular integrals that occur in many two dimensional applications of the boundary element method (e.g. potential theory and liner elasticity) can be treated in a unified manner by complex analysis. This paper presents an elegant approach for the evaluation of such hypersingular integrals. The limit to the boundary method, where a source point is moved from the inside (or outside) of a body to its boundary, is carried out using complex variables. The connection of this limit with the Hadamard Finite part of hypersingular integrals and principal value integrals is established. Many examples are worked out throughout the paper to illustrate the theory. Copyright 0 1996 Published by Elsevier Science Ltd.