ADMM ⊇ Projective Dynamics:
Fast Simulation of General Constitutive Models

Rahul Narain, Matthew Overby, George E. Brown
University of Minnesota

ACM SIGGRAPH / Eurographics Symposium on Computer Animation (SCA), 2016

Abstract: 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 demonstrate these benefits on several examples that include cloth, collisions, and volumetric deformable bodies with nonlinear elasticity.


 author = {Narain, Rahul and Overby, Matthew and Brown, George E.},
 title = {{ADMM} $\supseteq$ Projective Dynamics: Fast Simulation of General Constitutive Models},
 booktitle = {Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation},
 series = {SCA '16},
 year = {2016},
 isbn = {978-3-905674-61-3},
 location = {Zurich, Switzerland},
 pages = {21--28},
 numpages = {8},
 url = {},
 acmid = {2982822},
 publisher = {Eurographics Association},
 address = {Aire-la-Ville, Switzerland, Switzerland},