Parallel Multigrid for Nonlinear Cloth Simulation

Abstract

Accurate high‐resolution simulation of cloth is a highly desired computational tool in graphics applications. As single‐resolution simulation starts to reach the limit of computational power, we believe the future of cloth simulation is in multi‐resolution simulation. In this paper, we explore nonlinearity, adaptive smoothing, and parallelization under a full multigrid (FMG) framework. The foundation of this research is a novel nonlinear FMG method for unstructured meshes. To introduce nonlinearity into FMG, we propose to formulate the smoothing process at each resolution level as the computation of a search direction for the original high‐resolution nonlinear optimization problem. We prove that our nonlinear FMG is guaranteed to converge under various conditions and we investigate the improvements to its performance. We present an adaptive smoother which is used to reduce the computational cost in the regions with low residuals already. Compared to normal iterative solvers, our nonlinear FMG method provides faster convergence and better performance for both Newton's method and Projective Dynamics. Our experiment shows our method is efficient, accurate, stable against large time steps, and friendly with GPU parallelization. The performance of the method has a good scalability to the mesh resolution, and the method has good potential to be combined with multi‐resolution collision handling for real‐time simulation in the future.

Hierarchical Optimization Time Integration for CFL-Rate MPM Stepping

“…Multigrid methods [Briggs et al 2000] have been widely employed in accelerating existing computational frameworks for solving both solid [McAdams et al 2011;Tamstorf et al 2015;Tielen et al 2019;Wang et al 2018;Xian et al 2019;Zhu et al 2010] and fluid dynamics [Aanjaneya et al 2017;Fidkowski et al 2005;Gao et al 2018a;McAdams et al 2010;Setaluri et al 2014;Zhang and Bridson 2014;Zhang et al 2015Zhang et al , 2016. With multi-level structures, information of a particular cell can propagate faster to distant cells, making multigrid methods highly efficient for systems with long-range energy responses, or high stiffnesses.…”

“…Next, we observe that for each large-scale linear system solve in the inner loop of a Newton-Krylov method, classic Jacobi and Gauss-Seidel preconditioned CG solvers lose significant efficiency from slowed convergence as problem stiffnesses increase (Table 3). For such cases multigrid preconditioners [Tamstorf et al 2015;Wang et al 2018;Zhu et al 2010] are often effective solutions as the underlying hierarchy allows aggregation of multiple approximations of the system matrix inverse across a range of resolutions. This accelerates information propagation across the simulation domain, improving convergence.…”

Surface multigrid via intrinsic prolongation

“…In graphics, unstructured multigrid for 2D triangle meshes is widely applied to cloth simulation where the design pattern is prescribed by a 2D boundary curve. In the methods proposed in [Jeon et al 2013;Oh et al 2008;Wang et al 2018], they generate the hierarchy in a coarse-to-fine manner by triangulating the 2D design pattern and then recursively subdividing it to get finer resolutions. Wang et al [2018] generate the multigrid hierarchy from fine-to-coarse by clustering vertices on the fine mesh and re-triangulating the 2D domain.…”

“…In the methods proposed in [Jeon et al 2013;Oh et al 2008;Wang et al 2018], they generate the hierarchy in a coarse-to-fine manner by triangulating the 2D design pattern and then recursively subdividing it to get finer resolutions. Wang et al [2018] generate the multigrid hierarchy from fine-to-coarse by clustering vertices on the fine mesh and re-triangulating the 2D domain. When it comes to 3D tetrahedral meshes, multigrid is commonly used to simulate deformable objects.…”

Real-Time Augmented Reality Physics Simulator for Education

“…In this case, the parallel processing algorithm was designed to reconsider memory efficiency, and the performance was improved by about 400 times using the GPU, compared to using the CPU [11]. Wang et al presented an optimization method for high-resolution cloth simulation, and showed better performance for Newton's method and the projection dynamics method [12]. Our previous study evaluated the simulation performance of the CPU environment and the GPU environment through the experiment of freely dropping several 3D spheres, and showed that the performance of the GPU parallel processing environment is improved by about 84% [13,14].…”