A New Sigmoidal Transformation for Strongly Near-Singular Integrals over Triangular Elements

A sigmoidal transformation is applied to the singularity cancellation method to improve the numerical integration accuracy of strongly near-singular integrals over triangular elements. By employing the sigmoidal transformation, the quadrature points near to and distant from the singularity can both be redistributed to carry more information of the integrand. Improved accuracy and error convergence of typical strongly near-singular integrals are observed. To further increase the manipulation flexibility of the quadrature points, a new sigmoidal transformation is proposed in this letter. Several numerical results are presented to show the superiority of the proposed method.