Reducing Computational Costs of Small Steps Method in Projective Dynamics

Abstract

In this paper, we propose a method to reduce the computational complexity of the s Small Steps Method in Projective Dynamics, which is one of the elastic body simulation methods. The trade-off between the quality of the simulation and the amount of computation is always an issue in interactive computer graphics scenes. The Small Steps Method improves the simulation by reducing the numerical dumping by dividing the time evolution between drawing frames into small sub-steps instead of terminating the iterative computation for solving the problem in the middle. We note that the small-step method implicitly assumes the computation of sub-steps that are not drawn, and we omit the redundancy in the time direction. Specifically, we introduce DummyStep, a forward Eulerian method that uses acceleration to perform time evolution, and substitute DummyStep for half of the substeps in Projective Dynamics. As a result, Dummy Steps Method can replace the Small Steps Method with a very small error, and the computational complexity can be reduced by about half. However, since Dummy Steps Method has some stability problems, we propose two modification methods to further improve the stability of the method. Through example problems, we demonstrate that our method can stably replace the small step method while significantly reducing the computational complexity.