 
Summary: A matrixfree cone complementarity approach for solving largescale,
nonsmooth, rigid body dynamics
Preprint ANL/MCSP16921109
A.Tasora a
M.Anitescu b
aUniversit`a degli Studi di Parma, Dipartimento di Ingegneria Industriale, 43100 Parma, Italy, tasora@ied.unipr.it
bMathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA,
anitescu@mcs.anl.gov
Abstract
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 comple
mentarity problem by means of iterated fixedpoint 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 matrixfree 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.
Key words: Largescale multibody, contact, friction, cone complementarity problem
1. Introduction
Many engineering problems involve unilateral con
tacts between rigid bodies, for instance, in simulations
