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

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