Optimal coordinate transformations in numerical integrations of weakly singular and nearly singular integrals in BEMs

Abstract

The paper deals with an accurate numerical integration of the weakly singular and nearly singular integrals occuring in the BEM formulations. Optimal transformations of the integration variables are proposed in order to make the integrands to be distributed uniformly as much as possible over the whole integration area. Then, the integration can be performed with a sufficient accuracy by using standard integration quadratures without increasing the computational effort.