A binary-tree subdivision method for evaluation of singular integrals with discontinuous kernel in 3D BEM

Purpose A binary-tree subdivision method (BTSM) for numerical evaluation of weakly singular integrals with discontinuous kernel in the three-dimensional (3D) boundary element method (BEM) is presented in this paper. Design/methodology/approach In this method, the singular boundary element is split into two sub-elements and subdivided recursively until the termination criterion is met and the subdivision is stopped. Then, the source point is surrounded by one or more spherical cavities determined by the discontinuous kernel function. The sub-elements located in spherical cavities will be eliminated, and the regular triangular or rectangle elements are employed to fill the spherical cavities. Findings With the proposed method, the obtained sub-elements are automatically refined as they approach the source point, and they are “good” in shape and size for standard Gaussian quadrature. Thus, the proposed method can be used to evaluate singular integrals owing discontinuous kernel function accurately for cases of different element shapes and various source point locations. Originality/value Numerical examples show that the BTSM is suitable for planar and curved elements of arbitrary regular or irregular shape at various source point locations, and the results have much better accuracy and robustness than conventional subdivision method (CSM) when the kernel function is discontinuous.