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：物质点法是一种混合粒子-网格方法，广泛用于模拟具有历史依赖行为的大变形问题。标准物质点法通常依赖密集背景网格，当材料仅占据计算域一小部分时，这可能导致效率极低。这种稀疏性在许多大规模问题中常见，从地形大区域上的地球物理质量流到视觉计算应用。本文提出一种用于大规模物质点法模拟的统一稀疏背景网格框架。该框架将稀疏网格构建视为通用活动节点索引问题。我们开发了两种特定架构的实现来达成相同的稀疏框架：基于扫描的CPU策略和基于哈希的GPU策略。通过基准问题和大规模滑坡模拟，我们证明该框架在产生与标准密集物质点法相同结果的同时，在强稀疏情况下可将计算时间和内存使用降低一至两个数量级。