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

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 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.

Accelerating ADMM for efficient simulation and optimization

“…We apply our methods to a variety of ADMM solvers in graphics. We implement Anderson acceleration following the source code released by the authors of [Peng et al 2018] 1 . The source code of our implementation is available at https://github.com/bldeng/ AA-ADMM.…”

Learning‐Based Animation of Clothing for Virtual Try‐On

“…One example is a fast GPU‐based Gauss‐Seidel solver of constrained dynamics [FTP16]. Another example is the efficient handling of nonlinearities and dynamically changing constraints as a superset of projective dynamics [OBLN17]. Very recently, Tang et al .…”

“…One example is a fast GPU-based Gauss-Seidel solver of constrained dynamics [FTP16]. Another example is the efficient handling of nonlinearities and dynamically changing constraints as a superset of projective dynamics [OBLN17]. Very recently, Tang et al [TWL * 18] have designed a GPU-based solver of cloth dynamics with impact zones, efficiently integrated with GPU-based continuous collision detection.…”

Parallel and Scalable Heat Methods for Geodesic Distance Computation

“…Introducing M in the constraints does not alter the solution, but helps to make the algorithm robust to the mesh discretization. Indeed, a similar constraint reweighting strategy is employed in [29] to improve the convergence of their ADMM solver for physics simulation.…”