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Decomposed Optimization Time Integrator for Large-Step Elastodynamics

Basic Information

  • Title: Decomposed Optimization Time Integrator for Large-Step Elastodynamics
  • Authors: Minchen Li, Ming Gao, Timothy Langlois, Chenfanfu Jiang, Danny M. Kaufman
  • Affiliations: University of Pennsylvania & Adobe Research
  • Publication Date: July 2019
  • Journal: ACM Transactions on Graphics, Vol. 38, No. 4, Article 70
  • Keywords: Computational Optimization, Domain Decomposition, Large-Step Elastodynamics

Introduction

This paper presents the Decomposed Optimization Time Integrator (DOT), a novel domain-decomposed optimization method for solving per time step nonlinear problems of implicit numerical time integration in elastodynamics. It is particularly suited for simulations of deformable bodies with nonlinear materials and high-speed dynamics, efficiently solving large time step simulations with fixed-size steps, ensuring stable and high-quality simulation outputs.

Contributions

  • Introduction of DOT, an optimization method that employs a quadratic penalty decomposition to couple non-overlapping subdomains with weights derived from subdomain Hessian information.
  • Demonstration of DOT's efficiency, automation, and robustness for large fixed-size time steps, consistently converging to user-set tolerances and outperforming existing nonlinear time step solvers in both extreme and mild deformation dynamics.

Techniques and Method

DOT utilizes a domain-decomposed approach where the simulation domain is partitioned into non-overlapping subdomains. Each subdomain's Hessian is augmented with a quadratic penalty term that incorporates missing second-order information from neighboring subdomains. This quadratic penalty serves as an initializer for undecomposed L-BFGS time step solves on the full domain mesh, enabling efficient parallel computation and stable simulation progress.

Experimental Results

  • Extensive comparisons with recent performant nonlinear methods show DOT's superior performance across a range of deformation dynamics, significantly reducing wall-clock times for simulations.
  • The method is showcased in various scenarios, including large deformation dynamics of nonlinear materials, with DOT consistently achieving or exceeding the best performance metrics.

Limitations and Future Work

While the paper extensively demonstrates DOT's capabilities, it also acknowledges the potential for further optimization in solver efficiency and the exploration of more sophisticated line search and initialization techniques. Future directions include extending DOT's applicability to a broader range of physical phenomena and improving its scalability for even larger simulations.

Conclusion

DOT represents a significant advancement in the simulation of large-step elastodynamics, offering an efficient, automated, and robust method for high-quality simulations. Its domain-decomposition approach, combined with a novel penalty term for coupling subdomains, ensures stable progress across a wide array of challenging dynamics, setting a new standard for time integration in computational elastodynamics.