Iterative methods, Cone complementarity problems, LCP, Complementarity, Contacts, Multibody,

No 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 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.

We present a solution method that, compared to the traditional Gauss-Seidel approach, reduces the time required to simulate the dynamics of large systems of rigid bodies interacting through frictional contact by one to two orders of magnitude. Unlike Gauss-Seidel, it can be easily parallelized, which allows for the physics-based simulation of systems with millions of bodies. The proposed accelerated projected gradient descent (APGD) method relies on an approach by Nesterov in which a quadratic optimization problem with conic constraints is solved at each simulation time step to recover the normal and friction forces present in the system. The APGD method is validated against experimental data, compared in terms of speed of convergence and solution time with the Gauss-Seidel and Jacobi methods, and demonstrated in conjunction with snow modeling, bulldozer dynamics, and several benchmark tests that highlight the interplay between the friction and cohesion forces. . 2015.Using Nesterov's method to accelerate multibody dynamics with friction and contact.

In the context of simulating the frictional contact dynamics of large systems of rigid bodies, this paper reviews a novel method for solving large cone complementarity problems by means of a fixed-point iteration algorithm. The method is an extension of the Gauss-Seidel and Gauss-Jacobi methods with over-relaxation for symmetric convex linear complementarity problems. Convergent under fairly standard assumptions, the method is implemented in a parallel framework by using a single instruction multiple data computation paradigm promoted by the Compute Unified Device Architecture library for graphical processing unit programming. The framework supports the simulation of problems with more than one million bodies in contact. Simulation thus becomes a viable tool for investigating the dynamics of complex systems such as ground vehicles running on sand, powder composites, and granular material flow.