Parallel Efficiency of Lagrange Multipliers Based Divide and Conquer Algorithm for Dynamics of Multibody Systems

2011 ◽  
Author(s):  
Paweł Malczyk ◽  
Janusz Fra¸czek
Keyword(s):  
Parallel Computing ◽  
Lagrange Multipliers ◽  
Multibody Systems ◽  
Open Loop ◽  
Divide And Conquer ◽  
Dynamics Simulation ◽  
Parallel Computer ◽  
Optimal Order ◽  
Parallel Efficiency ◽  
Divide And Conquer Algorithm

Efficient dynamics simulations of complex multibody systems are essential in many areas of computer aided engineering and design. As parallel computing resources has become more available, researchers began to reformulate existing algorithms or to create new parallel formulations. Recent works on dynamics simulation of multibody systems include sequential recursive algorithms as well as low order, exact or iterative parallel algorithms. The first part of the paper presents an optimal order parallel algorithm for dynamics simulation of open loop chain multibody systems. The proposed method adopts a Featherstone’s divide and conquer scheme by using Lagrange multipliers approach for constraint imposition and dependent set of coordinates for the system state description. In the second part of the paper we investigate parallel efficiency measures of the proposed formulation. The performance comparisons are made on the basis of theoretical floating-point operations count. The main part of the paper is concetrated on experimental investigation performed on parallel computer using OpenMP threads. Numerical experiments confirm good overall efficiency of the formulation in case of modest parallel computing resources available and demonstrate certain computational advantages over sequential versions.

An Efficient Multibody Divide and Conquer Algorithm

2005 ◽  
Author(s):  
James H. Critchley
Keyword(s):  
Multibody Dynamics ◽  
Time Complexity ◽  
Future Generation ◽  
Parallel Computers ◽  
Parallel Processors ◽  
Divide And Conquer ◽  
Parallel Computer ◽  
Divide And Conquer Algorithm ◽  
Computer Resources ◽  
Theoretical Minimum

A new and efficient form of Featherstone’s multibody Divide and Conquer Algorithm (DCA) is presented. The DCA was the first algorithm to achieve theoretically optimal logarithmic time complexity with a theoretical minimum of parallel computer resources for general problems of multibody dynamics, however the DCA is extremely inefficient in the presence of small to modest parallel computers. The new efficient DCA approach (DCAe) demonstrates that large DCA subsystems can be constructed using fast sequential techniques and realize substantial speed increases in the presence of as few as two parallel processors. Previously the DCA was a tool intended for a future generation of parallel computers, this enhanced version promises practical and competitive performance with the parallel computers of today.

Multibody Dynamics in Generalized Divide and Conquer Algorithm (GDCA) Scheme

2011 ◽  
Author(s):  
Mohammad Poursina ◽  
Kurt S. Anderson
Keyword(s):  
Multibody Systems ◽  
Inverse Dynamics ◽  
Original System ◽  
Parent Body ◽  
Divide And Conquer ◽  
Loop Control ◽  
Generalized Coordinates ◽  
Divide And Conquer Algorithm ◽  
Generalized Force ◽  
New Formulation

Generalized divide and conquer algorithm (GDCA) is presented in this paper. In this new formulation, generalized forces appear explicitly in handle equations in addition to the spatial forces, absolute and generalized coordinates which have already been used in the original version of DCA. To accommodate these generalized forces in handle equations, a transformation is presented in this paper which provides an equivalent spatial force as an explicit function of a given generalized force. Each generalized force is then replaced by its equivalent spatial force applied from the appropriate parent body to its child body at the connecting joint without violating the dynamics of the original system. GDCA can be widely used in multibody problems in which a part of the forcing information is provided in generalized format. Herein, the application of the GDCA in controlling multibody systems in which the known generalized forces are fedback to the system is explained. It is also demonstrated that in inverse dynamics and closed-loop control problems in which the imposed constraints are often expressed in terms of generalized coordinates, a set of unknown generalized forces must be considered in the dynamics of system. As such, using both spatial and generalized forces, GDCA can be widely used to model these complicated multibody systems if it is desired to benefit from the computational advantages of the DCA.

Orthogonal Complement-Based Divide and Conquer Algorithm: A Detailed Investigation of Its Performance

2013 ◽  
Author(s):  
Imad M. Khan ◽  
Kurt S. Anderson
Keyword(s):  
Growth Rate ◽  
Arbitrary Number ◽  
Multibody Systems ◽  
Divide And Conquer ◽  
Orthogonal Complement ◽  
Error Growth ◽  
Stabilization Method ◽  
Constraint Violation ◽  
Divide And Conquer Algorithm ◽  
Kinematic Loops

In this paper, we characterize the orthogonal complement-based divide-and-conquer (ODCA) [1] algorithm in terms of the constraint violation error growth rate and singularity handling capabilities. In addition, we present a new constraint stabilization method for the ODCA architecture. The proposed stabilization method is applicable to general multibody systems with arbitrary number of closed kinematic loops. We compare the performance of the ODCA with augmented [2] and reduction [3] methods. The results indicate that the performance of the ODCA falls between these two traditional techniques. Furthermore, using a numerical example, we demonstrate the effectiveness of the new stabilization scheme.

Nano-Indentation Simulation Study Based on Parallel Computing

2012 ◽  
Vol 500 ◽  
pp. 696-701
Author(s):  
Ying Zhu ◽  
Sen Song ◽  
Ling Ling Xie ◽  
Shun He Qi ◽  
Qian Qian Liu
Keyword(s):  
Molecular Dynamics ◽  
Parallel Computing ◽  
Molecular Dynamics Simulation ◽  
Large Scale ◽  
Dynamics Simulation ◽  
Parallel Computer ◽  
Nano Indentation ◽  
Simulation Results ◽  
The Impact ◽  
Simulation Time

This method of parallel computing into nanoindentation molecular dynamics simulation (MDS), the author uses a nine-node parallel computer and takes the single crystal aluminum as the experimental example, to implement the large-scale process simulation of nanoindentation. Compared the simulation results with experimental results is to verify the reliability of the simulation. The method improves the computational efficiency and shortens the simulation time and the expansion of scale simulation can significantly reduce the impact of boundary conditions, effectively improve the accuracy of the molecular dynamics simulation of nanoindentation.

A Divide-and-Conquer Algorithm for Machining Feature Recognition Over Network

2005 ◽  
Author(s):  
Shuming Gao ◽  
Guangping Zhou ◽  
Yusheng Liu ◽  
Xiang Chen
Keyword(s):  
Parallel Computing ◽  
Feature Recognition ◽  
Feature Model ◽  
Divide And Conquer ◽  
Cad Model ◽  
Test Results ◽  
Machining Features ◽  
Divide And Conquer Algorithm ◽  
Machining Feature ◽  
Complex Parts

In this paper, a divide-and-conquer algorithm for machining feature recognition over network is presented. The algorithm consists of three steps. First, decompose the part and its stock into a number of sub-objects in the client and transfer the sub-objects to the server one by one. Meanwhile, perform machining feature recognition on each sub-object using the MCSG based approach in the server in parallel. Finally, generate the machining feature model of the part by synthesizing all the machining features including decomposed features recognized from all the sub-objects and send it back to the client. With divide-and-conquer and parallel computing, the algorithm is able to decrease the delay of transferring a complex CAD model over network and improve the capability of handling complex parts. Implementation details are included and some test results are given.

Efficient Operational Space Sensitivity Analysis of Dynamic Multibody Systems

2011 ◽  
Author(s):  
Rudranarayan M. Mukherjee
Keyword(s):  
Sensitivity Analysis ◽  
Data Storage ◽  
Multibody Systems ◽  
Parallel Implementation ◽  
Divide And Conquer ◽  
Parametric Perturbation ◽  
Divide And Conquer Algorithm ◽  
Operational Space ◽  
Tree Topologies ◽  
Logarithmic Complexity

This paper presents a generalization of the divide and conquer algorithm for sensitivity analysis of dynamic multibody systems based on direct differentiation. While similar sensitivity analysis approach has been demonstrated for multi-rigid and multi-flexible systems in tree topologies and a limited set of kinematically closed loop topologies, this paper presents the generalization of these approaches to systems in generalized topologies including many coupled kinematically closed loops. This generalization retains the efficient complexity of the underlying formulations i.e. linear and logarithmic complexity in serial and parallel implementation. Other than the computational efficiency, the advantages of this method include concurrent sensitivity analysis with forward dynamics, no numerical artifacts arising from parametric perturbation and significantly reduced data storage compared to traditional methods. An interesting application of this work in control of multibody systems is discussed.

Efficient Parallel Computer Simulation of the Motion Behaviors of Closed-Loop Multibody Systems

2007 ◽  
Author(s):  
Shanzhong Duan ◽  
Andrew Ries
Keyword(s):  
Parallel Computing ◽  
Multibody Systems ◽  
Closed Loop ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Parallel Computer ◽  
Constraint Forces ◽  
Computing Systems ◽  
Closed Loops

This paper presents an efficient parallelizable algorithm for the computer-aided simulation and numerical analysis of motion behaviors of multibody systems with closed-loops. The method is based on cutting certain user-defined system interbody joints so that a system of independent multibody subchains is formed. These subchains interact with one another through associated unknown constraint forces fc at the cut joints. The increased parallelism is obtainable through cutting joints and the explicit determination of associated constraint forces combined with a sequential O(n) method. Consequently, the sequential O(n) procedure is carried out within each subchain to form and solve the equations of motion while parallel strategies are performed between the subchains to form and solve constraint equations concurrently. For multibody systems with closed-loops, joint separations play both a role of creation of parallelism for computing load distribution and a role of opening a closed-loop for use of the O(n) algorithm. Joint separation strategies provide the flexibility for use of the algorithm so that it can easily accommodate the available number of processors while maintaining high efficiency. The algorithm gives the best performance for the application scenarios for n>>1 and n>>m, where n and m are number of degree of freedom and number of constraints of a multibody system with closed-loops respectively. The algorithm can be applied to both distributed-memory parallel computing systems and shared-memory parallel computing systems.

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