A. Tasora and M. Anitescu, "A Matrix-Free Cone Complementarity Approach for Solving Large-Scale, Nonsmooth, Ridig Body Dynamics," Preprint ANL/MCS-P1692-1109, November 2009. [pdf]
This paper proposes an iterative method that can simulate mechanical systems featuring a large number of contacts and joints between rigid bodies. The numerical method behaves as a contractive mapping that converges to the solution of a cone complementarity problem by means of iterated fixed-point steps with separable projections onto convex manifolds. Since computational speed and robustness are important issues when dealing with a large number of frictional contacts, we have performed special algorithmic optimizations in order to translate the numerical scheme into a matrix-free algorithm with O(n) space complexity and easy implementation. A modified version, that can run on parallel computers is discussed. A multithreaded version of the method has been used to simulate systems with more than a million contacts with friction.