A composite transformation for numerical integration of singular integrals in the BEM

In this paper we present a composite non-linear transformation of a polynomial transformation (PT) and a sigmoidal transformation (ST) by the name of CT PS (composite transformation with polynomial and sigmoidal transformations). This new transformation can be used for both Cauchy principal value (CPV) integrals and weakly singular integrals with interior singularities. Moreover, it is implied that the numerical evaluation using CT PS would be more e cient than either PT or ST used alone. By numerical examples, we show that the presented CT PS method, with the Gauss–Legendre quadrature rule, improves the approximation errors of the existing methods e ectively. In particular, it is demonstrated that the results of the present method are excellent for CPV integrals with near end point singularities