On the accuracy of the fast hierarchical DBEM for the analysis of static and dynamic crack problems

Abstract

In this paper the main features of a fast dual boundary element method based on the use of hierarchical matrices and iterative solvers are described and its effectiveness for fracture mechanics problems, both in the static and dynamic case, is demonstrated. The fast solver is built by representing the collocation matrix in hierarchical format and by using a preconditioned GMRES for the solution of the algebraic system. The preconditioner is computed in hierarchical format by LU decomposition of a coarse hierarchical representation of the collocation matrix. The method is applied to elastostatic problems and to elastodynamic cases represented in the Laplace transform domain. The application of the hierarchical format in the Laplace domain is straightforward and offers some interesting advantages related to the use of some local preconditioners. The accuracy in the determination of both static and dynamic stress intensity factors is assessed and the effectiveness of the technique is successfully demonstrated.