Optimal transformations of the integration variables in computation of singular integrals in BEM

The paper deals with numerical integrations of singular integrals in BEMs. It is shown that from the point of view of numerical integrations, the only serious problem which can arise is due to weakly singular and nearly singular integrals. We pay attention to the study of numerical integrations of nearly singular integrals by using transformations of the integration variables. Theoretical considerations and numerical experiments are performed for the integrals occurring in 2-D BEM formulations. The use of optimal transformation is confronted with the optimization of a polynomial transformation