Numerical evaluation of high-order singular boundary integrals using third-degree B-spline basis functions

Abstract

A novel method is presented for numerical evaluation of high-order singular boundary integrals that exist in the Cauchy principal value sense in two- and three-dimensional problems. In this method, three-dimensional boundary integrals are transformed into a line integral over the contour of the surface and a radial integral which contains singularities by using the radial integration method. The analytical elimination of singularities condensed in the radial integral formulas can be achieved by expressing the non-singular parts of the integration kernels as a series of cubic B-spline basis functions in the local distance  of the intrinsic coordinate system and using the intrinsic features of the radial integral. Some examples are provided to verify the correctness and robustness of the presented method.