A fast multipole boundary integral equation method for crack problems in 3D

This paper discusses a three-dimensional fast multipole boundary integral equation method for crack problems for Laplace's equation. The proposed implementation uses collocation and piecewise constant shape functions to discretise the hypersingular boundary integral equation for crack problems. The resulting numerical equation is solved with GMRES (generalised minimum residual method) in connection with FMM (fast multipole method). It is found that the obtained code is faster than a conventional one when the number of unknowns is greater than about 1300.