# Scalable and modular material point method for large-scale simulations

arXiv: https://arxiv.org/abs/1909.13380 · HTML: https://mlsanity.com/paper/1909.13380/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2019.

## Built on by (most cited first, 9 of 9)

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- [Accelerating Particle and Fluid Simulations with Differentiable Graph Networks for Solving Forward and Inverse Problems](https://mlsanity.com/paper/2309.13348/) (2023)
- [Inverse analysis of granular flows using differentiable graph neural network simulator](https://mlsanity.com/paper/2401.13695/) (2024)
- [JAX-MPM: A Learning-Augmented Differentiable Meshfree Framework for GPU-Accelerated Lagrangian Simulation and Geophysical Inverse Modeling](https://mlsanity.com/paper/2507.04192/) (2025)
- [Parameter-Efficient Conditioning for Material Generalization in Graph-Based Simulators](https://mlsanity.com/paper/2511.05456/) (2025)
- [Minority Report: A Graph Network Oracle for In Situ Visualization](https://mlsanity.com/paper/2206.12683/) (2022)
- [Three-dimensional granular flow simulation using graph neural network-based learned simulator](https://mlsanity.com/paper/2311.07416/) (2023)
- [MLPs and KANs for data-driven learning in physical problems: A performance comparison](https://mlsanity.com/paper/2504.11397/) (2025)
- [XDen-1K: A Density Field Dataset of Real-World Objects](https://mlsanity.com/paper/2512.10668/) (2025)

## Abstract (arXiv)

In this paper, we describe a new scalable and modular material point method (MPM) code developed for solving large-scale problems in continuum mechanics. The MPM is a hybrid Eulerian-Lagrangian approach, which uses both moving material points and computational nodes on a background mesh. The MPM has been successfully applied to solve large-deformation problems such as landslides, failure of slopes, concrete flows, etc. Solving these large-deformation problems result in the material points actively moving through the mesh. Developing an efficient parallelisation scheme for the MPM code requires dynamic load-balancing techniques for both the material points and the background mesh. This paper describes the data structures and algorithms employed to improve the performance and portability of the MPM code. An object-oriented programming paradigm is adopted to modularise the MPM code. The Unified Modelling Language (UML) diagram of the MPM code structure is shown in Figure 1.