Accelerated multiscale space–time finite element simulation and application to high cycle fatigue life prediction

A multiscale space–time finite element method based on time-discontinuous Galerkin and enrichment approach is presented in this work with a focus on improving the computational efficiencies for high cycle fatigue simulations. While the robustness of the TDG-based space–time method has been extensively demonstrated, a critical barrier for the extensive application is the large computational cost due to the additional temporal dimension and enrichment that are introduced. The present implementation focuses on two aspects: firstly, a preconditioned iterative solver is developed along with techniques for optimizing the matrix storage and operations. Secondly, parallel algorithms based on multi-core graphics processing unit are established to accelerate the progressive damage model implementation. It is shown that the computing time and memory from the accelerated space–time implementation scale with the number of degree of freedom N through \({\sim }\hbox {O}(N^{1.6})\) and \({\sim }\hbox {O}(N)\), respectively. Finally, we demonstrate the accelerated space–time FEM simulation through benchmark problems.