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In this paper, we introduce the Moving Least Squares Material Point Method (MLS-MPM). MLS-MPM naturally leads to the formulation of Affine Particle-In-Cell (APIC) and Polynomial Particle-In-Cell in a way that is consistent with a Galerkin-style weak form discretization of the governing equations. Additionally, it enables a new stress divergence discretization that effortlessly allows all MPM simulations to run two times faster than before. We also develop a Compatible Particle-In-Cell (CPIC) algorithm on top of MLS-MPM. Utilizing a colored distance field representation and a novel compatibility condition for particles and grid nodes, our framework enables the simulation of various new phenomena that are not previously supported by MPM, including material cutting, dynamic open boundaries, and two-way coupling with rigid bodies. MLS-MPM with CPIC is easy to implement and friendly to performance optimization.

    title={A Moving Least Squares Material Point Method with Displacement Discontinuity and Two-Way Rigid Body Coupling},
    author={Hu, Yuanming and Fang, Yu and Ge, Ziheng and Qu, Ziyin and Zhu, Yixin and Pradhana, Andre and Jiang, Chenfanfu},
    journal={Transaction on Graphics (TOG)},

We are grateful to the anonymous reviewers for their valuable suggestions and comments. We thank Christopher Long from Los Alamos National Laboratory for useful discussions, Hannah Bollar from University of Pennsylvania for narrating the video, and Hangxin Liu from UCLA CS Department for assisting the robot experiments. The work is partially supported by Jiang’s StartUp Grant from the University of Pennsylvania, NSF IIS-1755544, National Key Technology R&D Program of China (2017YFB1002701), a gift from Awowd Inc., a gift from NVIDIA Corporation, and a gift from SideFX.