Massively parallel phase field fracture simulations on supercomputers: towards multi-billion degree-of-freedom computations

An efficient parallel implementation of the phase field method for quasi-brittle crack simulations able to run on supercomputers with a large number of processes is proposed. This framework uses the finite-element method on 3D structured meshes, and was developed for distributed memory machines using the Message Passing Interface (MPI) for workload distribution and data communication between processes. Parallel assembly is carried out to build the matrices associated with the linear systems of equations. In the proposed context, linear systems derived from displacement and damage discretizations are solved using parallel solvers and preconditioners from the PETSc (Portable, Extensible Toolkit for Scientific Computation) library. All additional operations in this implementation are also efficiently parallelized. Performance analysis shows linear acceleration with an efficiency of \(97\%\) $97\%$ for a computation on 6400 processes and over \(80\%\) $80\%$ for a computation on 10240 processes. The linear systems involved in the simulations with up to \(10^{10}\) ${10}^{10}$ degrees of freedom can be solved in a few seconds. The methodology is applied to quasi-brittle simulations, involving alternate solving of large linear systems and incremental evolution. The applications presented to illustrate the parallel framework involve crack initiation and propagation in strongly heterogeneous materials with a detailed description of the microstructure. Large three-dimensional periodic structures and a realistic geometrical model directly obtained by micro-CT imagery are used.