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.

翻译：物质点法（MPM）是一种广泛用于模拟具有历史相关行为大变形问题的混合粒子-网格方法。标准MPM通常依赖稠密背景网格，当材料仅占据计算域的一小部分时，该方法的效率极低。这种稀疏性在许多大规模问题中普遍存在，从覆盖大型地形区域的地球物理质量流到视觉计算应用。本文针对大规模MPM模拟，提出了一种统一的稀疏背景网格框架。该框架将稀疏网格构建视为通用的活动节点索引问题。我们开发了两种特定架构的实现方式以实现相同的稀疏框架：针对CPU的基于扫描策略和针对GPU的基于哈希策略。通过基准测试问题和大规模滑坡模拟，我们证明该框架能够提供与标准稠密MPM相同的结果，同时在强稀疏情况下将计算时间和内存使用量降低一到两个数量级。