An adaptive element subdivision method for evaluation of weakly singular integrals in 3D BEM

A general adaptive element subdivision method is presented for the numerical evaluation of weakly singular integrals in three-dimensional boundary element analyses. In our method, the element is subdivided into a number of patches through a sequence of spheres with decreasing radius. The patches obtained by our method are automatically refined as they approach the source point. Consequently, each patch is “good” in shape and size for standard Gaussian quadrature, and hence high accuracy can be achieved by a small number of Gaussian sample points. Our method is applicable to any shape of element with arbitrary location of the source point inside, at vertices or on edges of the element. Numerical examples are presented for planar and curved surface elements. The results demonstrate that our method can provide much better accuracy and efficiency than the conventional subdivision method.