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

Area of Science:

• Computational physics
• Computer graphics
• Numerical analysis

Background:

• Implicit time integration is crucial for stable simulation of elastic bodies.
• Existing methods like projective dynamics offer speed but have limitations with complex models.
• General optimization algorithms can be adapted for physics simulation.

Purpose of the Study:

• To adapt the alternating direction method of multipliers (ADMM) for implicit time integration of elastic bodies.
• To leverage ADMM's general applicability for enhanced simulation capabilities.
• To extend the method for improved handling of dynamic constraints in simulations.

Main Methods:

• Application of the alternating direction method of multipliers (ADMM) optimization algorithm.
• Implicit time integration scheme for elastic body dynamics.
• Extension of ADMM to manage dynamically changing constraints like sliding and contact.

Main Results:

• The ADMM-based method shows close relation to projective dynamics.
• ADMM allows for nonlinear constitutive models and hard constraints.
• The extended algorithm maintains a constant system matrix for efficiency.
• Demonstrated effectiveness on cloth, collisions, and nonlinear volumetric bodies.

Conclusions:

• ADMM provides a robust, parallelizable, and efficient framework for simulating elastic bodies.
• The method extends projective dynamics capabilities to handle complex material models and interactions.
• This approach offers significant advantages for real-time simulation and complex physical phenomena.