A General Parallel Framework for Material Point Method Based on the p4est Library

Material Point Method(MPM) is widely used to simulate large deformation processes such as material fracture, collision, and fluid structure interaction. In general, an MPM simulation evolves a dynamic process in which a large number of Lagrangian particles move on top of Eulerian grids. During the process, physical quantities such as momentum and force are interpolated frequently between the particles and their corresponding grids. High Performance Computing(HPC) has become an indispensable tool for large-scale MPM simulations, while dynamic task decomposition and load balancing are critical for efficiency.In this paper, we present a general parallel framework integrating MPM and a well-established oct-tree mesh management library, p4est, aiming to improve the efficiency of large-scale MPM simulations. Through careful design of data structure and interfaces to connect the original Grid class of MPM with the p4est mesh, a highly modular structure is realized for the framework. This design allows the users to easily add new features or optimize existing ones, thereby enhancing its flexibility and reusability. On top of this, dynamic load-balancing strategies for MPM can be realized without much effort. A recommended strategy that considers both particle and grid workload is presented. In addition, the advantage of dynamic load balancing is demonstrated and analyzed through practical simulations. The versatility and efficiency of the proposed framework are also demonstrated through concrete real-world applications including penetration and building implosion simulations with up to 1.5 billion degrees of freedom. The code achieves 87% overall parallel efficiency scaling up to 2048 processors.