Parallel Computing in Multibody System Dynamics: Why, When, and How

Abstract

This paper addresses three questions related to the use of parallel computing in Multibody Dynamics (MBD) simulation. The "why parallel computing?" question is answered based on the argument that in the upcoming decade parallel computing represents the main source of speed improvement in MBD simulation. The answer to "when is it relevant?" is built around the observation that MBD software users are increasingly interested in multi-physics problems that cross disciplinary boundaries and lead to large sets of equations. The "how?" question is addressed by providing an overview of the state of the art in parallel computing. Emphasis is placed on parallelization approaches and support tools specific to MBD simulation. Three MBD applications are presented where parallel computing has been used to increase problem size and/or reduce time to solution. The paper concludes with a summary of best practices relevant when mapping MBD solutions onto parallel computing hardware.

Distributed parallel computing of the recursive eigenvalue search in the context of transfer matrix method for multibody systems

“…It is worth mentioning that the order of the coefficient matrix U all is very low, which will not cost too much time in computation of determinant det U all . From equation (4), it can also be found that the characteristic equation is a nonlinear or even transcendental function w.r.t. the eigenvalue.…”

“…Then the eigenvalue v of the system can be acquired by solving equation (4). For a multibody system in a more generic topology, the overall transfer equation and the overall transfer matrix can be obtained by simply following the automatic deduction theorem of the overall transfer equation for multibody systems 11 taking a general form…”

Efficient and accurate modeling of rigid rods

“…By using the augmented Lagrangian technique to avoid numerical ill-conditioning, accurate solutions were obtained. Other approaches for the improvement of computational efficiency are based on the advances of parallelization technology [1,2,5,17,18]. García de Jalón et al [10,12,20] developed an alternative formulation of the equations of motion in terms of independent coordinates.…”

A parallel Hamiltonian formulation for forward dynamics of closed-loop multibody systems

“…One can encounter applications like that in such areas as robotics, biomechanics, and automotive industry. The other places where one needs efficient MBS simulations can be found in various interdisciplinary applications like, e.g., molecular dynamics simulations [1,2] or granular media physics [3]. The applications are more complex and demanding.…”

“…In [19], Critchley and Anderson explored the notion of recursive coordinate reduction. There are other works associated with parallel multibody dynamics simulations as well [3,20,21]. Recently, the divide-and-conquer based schemes [17] have attracted significant attention to the development of efficient parallel algorithms for large MBS, partially due to the fact that computationally powerful multicore processors or graphics processor units are cheaply available on the market.…”