ON NONLINEAR TRANSFORMATIONS FOR THE INTEGRATION OF WEAKLY-SINGULAR AND CAUCHY PRINCIPAL VALUE INTEGRALS

The mathematical foundations of the application of non-linear transfor mations to the numerical integration of weakly singular and Cauchy Pri ncipal Value (CPV) integrals are revised in this paper. This approach was firstly introduced to compute the singular kernels appearing in th e Boundary Element Method (BEM) for 2-D (two-dimensional) problems. He re, the mathematical requirements for a consistent application of thes e methods both for the 2-D and 3-D cases and both for collocation poin ts located in the interior of a typical boundary element and located o n its boundary are established. From them, it is shown why some of the transformations proposed in previous papers work while others do not, and also why some of the latter ones work only for the particular exa mples presented in those papers. Finally, some non-linear transformati ons for 2-D and 3-D problems that fulfill the mentioned mathematical r equirements are here introduced, including a complete numerical study of their accuracy. (C) 1997 by John Wiley & Sons, Ltd.