TY - JOUR
T1 - ADMM ⊇ Projective Dynamics
T2 - Fast Simulation of Hyperelastic Models with Dynamic Constraints
AU - Overby, Matthew
AU - Brown, George E.
AU - Li, Jie
AU - Narain, Rahul
N1 - Publisher Copyright:
© 1995-2012 IEEE.
PY - 2017/10/1
Y1 - 2017/10/1
N2 - 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.
AB - 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.
KW - Computer graphics
KW - animation
KW - computer simulation
KW - dynamics
KW - optimization methods
UR - http://www.scopus.com/inward/record.url?scp=85028821124&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85028821124&partnerID=8YFLogxK
U2 - 10.1109/TVCG.2017.2730875
DO - 10.1109/TVCG.2017.2730875
M3 - Article
C2 - 28742041
AN - SCOPUS:85028821124
SN - 1077-2626
VL - 23
SP - 2222
EP - 2234
JO - IEEE Transactions on Visualization and Computer Graphics
JF - IEEE Transactions on Visualization and Computer Graphics
IS - 10
M1 - 7990052
ER -