An efficient parallel solution scheme for the phase field approach to dynamic fracture based on a domain decomposition method

The phase field approach to fracture becomes popular for complicated fracture problems in recent years. However, its widespread application is hindered by its high computational cost. In this article, we propose an efficient parallel explicit-implicit solution scheme for the phase field approach to dynamic fracture based on a domain decomposition method, specifically, the dual-primal finite element tearing and interconnecting (FETI-DP) method. In this scheme, the displacement field is updated by an explicit algorithm in parallel, and the phase field is implicitly solved by the FETI-DP method. In particular, Lagrange multipliers are introduced to ensure the interface continuity of the phase field. In the computational process, the information exchange among subdomains merely exists in a few substeps, which renders the cost for communication very small. Moreover, the size of equations to be solved is proportional to the total area of subdomain interfaces, which is significantly reduced compared with a typical single-domain solution procedure. The solution scheme is able to perform phase field simulations with a million of degrees of freedom using only 0.034 core hours per load step, and has flexible extensibility for existing phase field codes. Several numerical examples demonstrate the accuracy and efficiency of the proposed scheme.