Partial integration based regularization in BEM for 3D elastostatic problems: The role of line integrals

The Boundary Element Method (BEM) is a powerful numerical approach for solving 3D elastostatic problems, particularly useful for crack propagation in fracture mechanics and half-space problems. A key challenge in BEM lies in handling singular integral kernels. Various analytical and numerical integration or regularization techniques address this, including one that combines partial integration with Stokes' theorem to reduce hyper-singular and strong singular kernels to weakly singular ones. This approach typically assumes a closed surface, omitting the boundary integrals from Stokes' theorem. In this paper, these usually neglected boundary line integrals are introduced and their significance is demonstrated, first in a pure half-space problem, and then shown to be redundant in fast multipole method (FMM) based BEM, where geometry partitioning produces pseudo open surfaces.