Sparsity Exploitation of Accelerated Modulus-Based Gauss-Seidel Method for Interactive Rigid Body Simulations

TL;DR

This paper introduces a sparsity-exploiting, accelerated modulus-based Gauss-Seidel method tailored for large-scale linear complementarity problems in interactive rigid-body simulations, improving efficiency and accuracy over existing methods.

Contribution

The paper presents a novel, sparsity-aware, accelerated modulus-based Gauss-Seidel method specifically designed for large-scale LCPs in rigid-body simulations, enhancing computational efficiency and accuracy.

Findings

The proposed method outperforms simple applications of existing accelerated methods.

It demonstrates superior accuracy per iteration compared to the projected Gauss-Seidel method.

Numerical experiments confirm improved efficiency for large-scale problems.

Abstract

Large-scale linear complementarity problems (LCPs) are repeatedly solved in interactive rigid-body simulations. The projected Gauss-Seidel method is often employed for LCPs, since it has advantages in computation time, numerical robustness, and memory use. Zheng and Yin (2013) proposed modulus-based matrix splitting iteration methods and showed their effectiveness for large problems, but a simple application of their approach to large-scale LCPs in interactive rigid-body simulations is not effective since such a simple application demands large matrix multiplications. In this paper, we propose a novel method derived from accelerated modulus-based matrix splitting iteration methods that fits LCPs arising in interactive rigid-body simulations. To improve the computation time, we exploit sparsity structures related to the generalized velocity vector of rigid bodies. We discuss the convergence of the proposed method for an important case that the coefficient matrix of a given LCP is a positive definite matrix. Numerical experiments show that the proposed method is more efficient than the simple application of the accelerated modulus-based Gauss-Seidel method and that the accuracy in each step of the proposed method is superior to that of the projected Gauss-Seidel method.