Hierarchical Optimization Time Integration for CFL-rate MPM Stepping

TL;DR

This paper introduces HOT, a hierarchical optimization algorithm for implicit MPM time-stepping that is efficient, robust, and adaptable across various materials and conditions, significantly outperforming existing methods.

Contribution

HOT is a novel hierarchical optimization approach tailored for implicit MPM, providing out-of-the-box convergence and high parallel efficiency without parameter tuning.

Findings

HOT achieves up to 10x speedup over existing codes.

HOT maintains performance across diverse materials and deformation scenarios.

Alternative methods exhibit severe issues and poor performance.

Abstract

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.