ADMM ⊇ Projective Dynamics: Fast Simulation of Hyperelastic Models with Dynamic Constraints

Matthew Overby, George E. Brown, Jie Li, Rahul Narain

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


We apply the alternating direction method of multipliers (ADMM) optimization algorithm to implicit time integration of elastic bodies, and show that the resulting method closely relates to the recently proposed projective dynamics algorithm. However, as ADMM is a general purpose optimization algorithm applicable to a broad range of objective functions, it permits the use of nonlinear constitutive models and hard constraints while retaining the speed, parallelizability, and robustness of projective dynamics. We further extend the algorithm to improve the handling of dynamically changing constraints such as sliding and contact, while maintaining the benefits of a constant, prefactored system matrix. We demonstrate the benefits of our algorithm on several examples that include cloth, collisions, and volumetric deformable bodies with nonlinear elasticity and skin sliding effects.

Original languageEnglish (US)
Article number7990052
Pages (from-to)2222-2234
Number of pages13
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number10
StatePublished - Oct 1 2017

Bibliographical note

Publisher Copyright:
© 1995-2012 IEEE.


  • Computer graphics
  • animation
  • computer simulation
  • dynamics
  • optimization methods


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