WIT Press


Numerical Evaluation Of High-order Singular Boundary Integrals Using Third-degree B-spline Basis Functions

Price

Free (open access)

Paper DOI

10.2495/BEM360141

Volume

56

Pages

13

Page Range

153 - 165

Published

2014

Size

398 kb

Author(s)

Jinxiu Hu, Baojing Zheng & Xiaowei Gao

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. Keywords: singular integrals, boundary element method, radial integration method, Cauchy principal value, B-spline basis function.

Keywords

singular integrals, boundary element method, radial integration method, Cauchy principal value, B-spline basis function