Unified sparse framework for large-scale material point method simulations

2026-05-27

AI Summary

This work addresses the inefficiency of the standard Material Point Method (MPM) in large-scale simulations where material occupies only a small fraction of the computational domain, due to its reliance on dense background grids. The authors propose a unified sparse background grid framework that formulates sparsity as a general active-node indexing problem and introduces tailored, high-performance implementations for both CPU and GPU architectures—based on scan and hash-based strategies, respectively. This approach maintains simulation accuracy while dramatically improving computational and memory efficiency in sparse scenarios. Under strong sparsity conditions, it reduces both runtime and memory consumption by one to two orders of magnitude compared to conventional dense MPM, with excellent consistency in results.

Abstract

The material point method (MPM) is a hybrid particle-grid method widely used for simulating large deformation with history-dependent behavior. Standard MPM often relies on a dense background grid, which can be highly inefficient when material occupies a small fraction of the computational domain. Such sparsity is common in many large-scale problems, from geophysical mass flows over large terrain domains to visual-computing applications. Here, we introduce a unified sparse background-grid framework for large-scale MPM simulation. The framework treats sparse grid construction as a general active-node indexing problem. We develop two architecture-specific implementations to realize the same sparse framework: a scan-based strategy for CPUs and a hash-based strategy for GPUs. Through benchmark problems and a large-scale landslide simulation, we show that the framework provides the same results as standard dense MPM while reducing computational time and memory usage by one to two orders of magnitude in strongly sparse cases.

Problem

• material point method
• sparse grid
• large-scale simulation
• computational efficiency
• background grid

Innovation

• sparse grid
• material point method
• active-node indexing
• CPU/GPU optimization
• large-scale simulation