Numerical Evaluation Of High-order Singular Boundary Integrals Using Third-degree B-spline Basis Functions
Free (open access)
153 - 165
Jinxiu Hu, Baojing Zheng & Xiaowei Gao
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. Keywords: singular integrals, boundary element method, radial integration method, Cauchy principal value, B-spline basis function.
singular integrals, boundary element method, radial integration method, Cauchy principal value, B-spline basis function