Abstract:
Boundary element method (BEM) has been widely used for solving the practical engineering problems. Accurate and efficient evaluation of singular integral is of crucial importance for solving the boundary integral equations. In the BEM implementation, an adaptive element subdivision method for singular integrals based on affine transformations is presented for evaluating the singular integrals. The basic idea consists of partitioning the input surface element via affine transformation and then generating a set of high-quality patches by adaptive binary-tree subdivision. By using the domain partitioning technique, the surface element can be divided into several element projection and subdivision regions under affine transformations. It is far more efficient to separately perform the element subdivision for different regions where the desirable patches are required. The ultimate sub-elements in the vicinity of the singular point are constructed by the serendipity patches, while the remaining patches are evaluated accurately by the conventional quadrature techniques. The proposed method has some advantages over the conventional element subdivision methods, such as the adaptive element subdivision, the improved accuracy and the straight-forward implementation. Numerical results are provided to validate the accuracy, robustness and availability of the proposed method.