Hierarchical Optimization Time Integration for CFL-rate MPM Stepping
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We propose Hierarchical Optimization Time Integration (HOT) for efficient implicit time stepping of the Material Point method (MPM) irrespective of simulated materials and conditions. HOT is a MPM-specialized hierarchical optimization algorithm that solves nonlinear time step problems for large-scale MPM systems near the CFL-limit, e.g., with step sizes around 0.01s. HOT provides "out-of-the-box" convergent simulations across widely varying materials and computational resolutions without parameter tuning. As the first MPM solver enhanced by h-multigrid, HOT is highly parallelizable and, as we show in our analysis, robustly maintains consistent and efficient performance even as we grow stiffness, increase deformation, and vary materials over a wide range of finite strain, elastodynamic and plastic examples. Through careful benchmark ablation studies, we compare the effectiveness of HOT against seemingly plausible alternative combinations of MPM with standard multigrid and other Newton-Krylov models. We show how these alternative designs result in severe issues and poor performance. In contrast, HOT outperforms existing state-of-the-art, heavily optimized implicit MPM codes with an up to 10x performance speedup across a wide range of challenging benchmark test simulations.
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