Fast multipole method applied to Symmetric Galerkin boundary element method for 3D elasticity and fracture problems

The solution of three-dimensional elastostatic problems using the Symmetric Galerkin Boundary Element Method (SGBEM) gives rise to fully populated (albeit symmetric) matrix equations, entailing high solution times for large models. This paper is concerned with the formulation and implementation of a multi-level fast multipole SGBEM (FM-SGBEM) for elastic solid with cracks. Arbitrary geometries and boundary conditions may be considered. Numerical results on test problems involving a cube, single or multiple cracks in an unbounded medium, and a cracked cylindrical solid are presented. BEM models involving up to 10 ⁶ BEM unknowns are considered, and the desirable predicted trends of the elastostatic FM-SGBEM, such as a O(N) complexity per iteration, are verified.