Index-3 divide-and-conquer algorithm for efficient multibody system dynamics simulations: theory and parallel implementation

Abstract

There has been a growing attention to efficient simulations of multibody systems, which is apparently seen in many areas of computer-aided engineering and design both in academia and in industry. The need for efficient or real-time simulations requires highfidelity techniques and formulations that should significantly minimize computational time. Parallel computing is one of the approaches to achieve this objective. This paper presents a novel index-3 divide-andconquer algorithm for efficient multibody dynamics simulations that elegantly handles multibody systems in generalized topologies through the application of the augmented Lagrangian method. The proposed algorithm exploits a redundant set of absolute coordinates. The trapezoidal integration rule is embedded into the formulation and a set of nonlinear equations need to be solved every time instant. Consequently, the Newton-Raphson iterative scheme is applied to find the system

Parallel Computations and Co-Simulation in Universal Mechanism Software. Part I: Algorithms and Implementation

“…It is important that for the stiff forces, used in simulation of rail vehicles, the matrix composed of the approximate JM is negative semidefinite [26,27]. Substitution of Equations (7-9) in ( 5) yields linear equations relative to the unknown values (10) with the set of stiff force indices for body i, the positive definite matrix (11) and the vector summarizing all forces (12) The PCGM [28,29] is suitable for parallel solving Equations ( 10) and the matrix is highly efficient as the preconditioning matrix in this algorithm. To explain this statement, consider Equations (10) in the full matrix form According to a theorem proved in Pogorelov [26], the spectral radius of the matrix is less than 1, .…”

“…they require O(log N) operations in simulation of an articulated MBS with N rigid bodies on N processors. DCA, CFA and further developments of these algorithms [5][6][7][8][9][10] do not support implicit solver procedures for stiff MBS, which limits their application to simulation of rail vehicle dynamics.…”

FPGA acceleration of planar multibody dynamics simulations in the Hamiltonian–based divide–and–conquer framework

“…The computational expenses spent by many existing multibody algorithms are high and usually do not exploit current computer hardware platforms to the extent possible [3]. The mentioned issues imply that researchers pay more and more attention to the development of parallel algorithms and formulations for modeling and analysis of MBS, including real-time simulations, e.g., [4], [5], [6], [7], [8], [9], [10].…”

“…Its binary-tree structure allows distributing the computations among several processing cores in a scalable, logarithmic way. So far, several practical implementations of the divide-and-conquer algorithm have been developed on multicore CPUs [10] and GPUs [26].…”

A regularization method for solving dynamic problems with singular configuration

“…For the augmented Lagrangian method, the selection of the numerical integrator and penalty parameters has much influence on the robustness and accuracy of the simulations. 18,19 In reference, 10 a time-stepping algorithm was built by combining the index-three ALF with mass projections and Newmark integration method, which shows good behavior. Using the null space of the Jacobian matrix, an efficient dynamic formulation with a relatively compact form was presented and the solution can be solved in a closed-form manner even in the existence of singular or redundant constraints, as the inertial matrix of the constraints always has full rank.…”