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 an MPM-specialized hierarchical optimization algorithm that solves nonlinear time step problems for large-scale MPM systems near the CFL-limit. HOT provides convergent simulations "out-of-the-box" across widely varying materials and computational resolutions without parameter tuning. As an implicit MPM time stepper accelerated by a custom-designed Galerkin multigrid wrapped in a quasi-Newton solver, HOT is both highly parallelizable and robustly convergent. As we show in our analysis, HOT 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 the 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.

中文翻译：

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CFL 速率 MPM 步进的分层优化时间积分

我们提出了分层优化时间积分 (HOT)，以实现材料点法 (MPM) 的有效隐式时间步长，而不管模拟材料和条件如何。HOT 是一种 MPM 专用分层优化算法，用于解决接近 CFL 极限的大规模 MPM 系统的非线性时间步长问题。HOT 提供了“开箱即用”的收敛模拟，无需参数调整即可跨越广泛变化的材料和计算分辨率。作为由包裹在准牛顿求解器中的定制设计的 Galerkin 多重网格加速的隐式 MPM 时间步进器，HOT 具有高度并行性和稳健收敛性。正如我们在分析中所展示的，即使我们在很宽的有限应变范围内增加刚度、增加变形和改变材料，HOT 也能保持一致和高效的性能，弹性动力学和塑性示例。通过仔细的基准消融研究，我们将 HOT 的有效性与 MPM 与标准多重网格和其他 Newton-Krylov 模型的看似合理的替代组合进行了比较。我们展示了这些替代设计如何导致严重的问题和糟糕的性能。相比之下，HOT 的性能优于现有的最先进的、经过高度优化的隐式 MPM 代码，在各种具有挑战性的基准测试模拟中性能提升高达 10 倍。