Browsing by Author "Schroeder, Craig"

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    Effective Time Step Restrictions for Explicit MPM Simulation
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Sun, Yunxin; Shinar, Tamar; Schroeder, Craig; Bender, Jan and Popa, Tiberiu
    Time steps for explicit MPM simulation in computer graphics are often selected by trial and error due to the challenges in automatically selecting stable time step sizes. Our time integration scheme uses time step restrictions that take into account forces, collisions, and even grid-to-particle transfers calculated near the end of the time step. We propose a novel set of time step restrictions that allow a time step to be selected that is stable, efficient to compute, and not too far from optimal. We derive the general solution for the sound speed in nonlinear isotropic hyperelastic materials, which we use to enforce the classical CFL time step restriction. We identify a single-particle instability in explicit MPM integration and propose a corresponding time step restriction in the fluid case. We also propose a reflection-based boundary condition for domain walls that supports separation and accurate Coulomb friction while preventing particles from penetrating the domain walls.
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    Stability Analysis of Explicit MPM
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Bai, Song; Schroeder, Craig; Dominik L. Michels; Soeren Pirk
    In this paper we analyze the stability of the explicit material point method (MPM). We focus on PIC, APIC, and CPIC transfers using quadratic and cubic splines in two and three dimensions. We perform a fully three-dimensional Von Neumann stability analysis to study the behavior within the bulk of a material. This reveals the relationship between the sound speed, CFL number, and actual time step restriction and its dependence on discretization options. We note that boundaries are generally less stable than the interior, with stable time steps generally decreasing until the limit when particles become isolated. We then analyze the stability of a single particle to derive a novel time step restriction that stabilizes simulations at their boundaries. Finally, we show that for explicit MPM with APIC or CPIC transfers, there are pathological cases where growth is observed at arbitrarily small time steps sizes. While these cases do not necessarily pose a problem for practical usage, they do suggest that a guarantee of stability may be theoretically impossible and that necessary but not sufficient time step restrictions may be a necessary and practical compromise.