Simple Sparse Grid for Efficient Simulation of Large-scale Mass Flows Using the Material Point Method
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The material point method (MPM) has been widely used for simulating mass flows. However, many MPM implementations face significant challenges in high-fidelity, large-scale simulations. A main computational bottleneck arises from the use of a globally dense background grid that must cover the entire potential flow domain. This leads to severe memory overhead and significantly reduces computational efficiency. In this work, we introduce a simple hash-table-based sparse grid approach that dynamically activates only the grid nodes involved in particle–grid interactions. Compared with existing sparse MPM frameworks, the proposed method is lightweight and easy to implement, requiring no or only minimal external dependencies. Moreover, unlike existing GPU-based sparse approaches that are restricted to specific hardware architectures, our approach can be applied consistently on both CPU and GPU platforms. The proposed framework is tested on both GPU[1] and CPU[2]. They demonstrate orders-of-magnitude performance improvements compared with naive dense-grid implementations. Because of its simplicity, the proposed sparse strategy is particularly well-suited for large-scale landslide modeling and can be easily integrated into existing in-house MPM codes. REFERENCES [1] Zhao, Y., Li, X., Jiang, C., & Choo, J. (2026). GeoWarp: An automatically differentiable and GPU-accelerated implicit MPM framework for geomechanics based on NVIDIA Warp. Advances in Engineering Software, 212, 104072. [2] Blatny, L., & Gaume, J. (2025). Matter (v1): An open-source MPM solver for granular matter. Geoscientific Model Development, 18(22), 9149-9166.
