DOMAIN DECOMPOSITION METHODS FOR CRACK GROWTH PROBLEMS USING XFEM

Abstract

. The extended finite element method (XFEM) enriches the polynomial basis functions of standard finite elements with specialized non-smooth functions. The resulting approximation space can be used to solve problems with moving discontinuities, such as cracks, while avoiding the computational cost of remeshing. As the crack propagates, many artificial degrees of freedom are introduced near the crack tip, which can inflate the size of resulting linear system to be solved. In addition, the stiffness matrix of the cracked body may become ill-conditioned, causing slow convergence of iterative solvers. To overcome this, domain decomposition methods for solving the resulting linear systems of crack propagation problems is combined with XFEM to improve its performance. A suitable decomposition is proposed to avoid inter-subdomain boundaries near crack tip area. It is shown that choosing the proper FETI method, offers significant speedup compared to a direct solver that uses the common finite element solution techniques by means of Cholesky/LDL factorization, even if the execution is performed on a single-core systems.