Unified sparse framework for large-scale simulations using the material point method

Abstract. The material point method (MPM) is a hybrid particle-grid method widely used for large deformation problems with history-dependent behavior, including geophysical mass flows. 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 geophysical mass flow problems. 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 identical results as standard dense MPM while reducing computational time and memory usage by one to two orders of magnitude in strongly sparse cases.