Decomposed Optimization Time Integrator for Large-Step Elastodynamics

Minchen Li1,2Ming Gao1Timothy Langlois2Chenfanfu Jiang1Danny M. Kaufman2
1University of Pennsylvania,  2Adobe Research
ACM Transactions on Graphics (SIGGRAPH), 2019
Severe deformation dynamics simulated with large steps. (a) The Decomposed Optimization Time Integrator (DOT) decomposes spatial domains to generate high-quality simulations of nonlinear materials undergoing large-deformation dynamics. In (b) we apply DOT to rapidly stretch and pull an Armadillo backwards. We render in (c) a few frames of the resulting slingshot motion right after release. DOT efficiently solves time steps while achieving user-specified accuracies --- even when stepping at frame-rate size steps; here at 25 ms. In (d) we emphasize the large steps taken by rendering all DOT-simulated time steps from the Armadillo's high-speed trajectory for the first few moments after release.

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Simulation methods are rapidly advancing the accuracy, consistency and controllability of elastodynamic modeling and animation. Critical to these advances, we require efficient time step solvers that reliably solve all implicit time integration problems for elastica. While available time step solvers succeed admirably in some regimes, they become impractically slow, inaccurate, unstable, or even divergent in others --- as we show here. Towards addressing these needs we present the Decomposed Optimization Time Integrator (DOT), a new domain-decomposed optimization method for solving the per time step, nonlinear problems of implicit numerical time integration. DOT is especially suitable for large time step simulations of deformable bodies with nonlinear materials and high-speed dynamics. It is efficient, automated, and robust at large, fixed-size time steps, thus ensuring stable, continued progress of high-quality simulation output. Across a broad range of extreme and mild deformation dynamics, using frame-rate size time steps with widely varying object shapes and mesh resolutions, we show that DOT always converges to user-set tolerances, generally well-exceeding and always close to the best wall-clock times across all previous nonlinear time step solvers, irrespective of the deformation applied.

Source Code and Data
  author  = {Minchen Li and Ming Gao and Timothy Langlois and Chenfanfu Jiang and Danny M. Kaufman},
  title   = {Decomposed Optimization Time Integrator for Large-Step Elastodynamics},
  journal = {ACM Transactions on Graphics},
  year    = {2019},
  volume = {38},
  number = {4},
  publisher = {ACM}
Supplemental Document