An isogeometric boundary element method using adaptive integral method for 3D potential problems

- A general method is proposed to calculate the nearly singular integrals appearing in the 3D IGABEM.
- The boundary element integrations can be computed easily and effectively at optimal computational cost.
- The adaptive algorithm can be used to cope with the common situation where the sizes of adjacent cells are significantly different.
- The power series expansion method is expanded to compute the singular integrals appearing in 3D IGABEM.

Due to the merits of exact geometrical representation, high accuracy, no meshing process, and only the boundary description of the problem etc., the isogeometric boundary element method, i.e. IGABEM, has achieved rapid development. In this paper, based on the upper bound of the relative error of the Gaussian quadrature formula, we presented a 3D IGABEM using adaptive integration method for potential problems. This method offers a number of key improvements compared with conventional IGABEM. Firstly, the boundary element integrations can be computed easily and effectively at optimal computational cost. Secondly, the adaptive algorithm can cope with the common situation where the sizes of adjacent cells are significantly different. Moreover, the presented method can compute the nearly singular integrals easily, owing to the use of subdivision technique. To accurately evaluate the singular integrals appearing in our method, the power series expansion method is employed. The integration surface is on the real surface of the model, rather than the interpolation surface, i.e. no geometrical errors. Thus, the value of integral is more accurate than the traditional boundary element method, which can improve the computation accuracy of the IGABEM. Numerical tests show that the presented method has good performance in both exactness and convergence.