Descent Methods for Elastic Body Simulation on the GPU

摘要

We show that many existing elastic body simulation approaches canrnbe interpreted as descent methods, under a nonlinear optimizationrnframework derived from implicit time integration. The key questionrnis how to find an eu000bective descent direction with a low computationalrncost. Based on this concept, we propose a new gradient descentrnmethod using Jacobi preconditioning and Chebyshev acceleration.rnThe convergence rate of this method is comparable to that of LBFGSrnor nonlinear conjugate gradient. But unlike other methods, itrnrequires no dot product operation, making it suitable for GPU implementation.rnTo further improve its convergence and performance,rnwe develop a series of step length adjustment, initialization, andrninvertible model conversion techniques, all of which are compatiblernwith GPU acceleration. Our experiment shows that the resultingrnsimulator is simple, fast, scalable, memory-eu000ecient, and robustrnagainst very large time steps and deformations. It can correctlyrnsimulate the deformation behaviors of many elastic materials, asrnlong as their energy functions are second-order diu000berentiable andrntheir Hessian matrices can be quickly evaluated. For additionalrnspeedups, the method can also serve as a complement to otherrntechniques, such as multi-grid.