Research Papers

An Efficient Multibody Divide and Conquer Algorithm and Implementation

[+] Author and Article Information
James H. Critchley

 BAE Systems, Troy, MI 48384

Kurt S. Anderson1

Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180-3590anderk5@rpi.edu

Adarsh Binani

 The Math Works, Natick, MA 01760adarsh.binani@gmail.com


Corresponding author.

J. Comput. Nonlinear Dynam 4(2), 021004 (Mar 06, 2009) (10 pages) doi:10.1115/1.3079823 History: Received September 28, 2007; Revised June 16, 2008; Published March 06, 2009

A new and efficient form of Featherstone’s multibody divide and conquer algorithm (DCA) is presented and evaluated. The DCA was the first algorithm to achieve theoretically the 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. This alternative efficient DCA (DCAe) approach demonstrates that large DCA subsystems can be constructed using fast sequential techniques to realize a substantial increase in speed. The usefulness of the DCAe is directly demonstrated in an application to a four processor workstation and compared with the results from the original DCA and a fast sequential recursive method. Previously the DCA was a tool intended for a future generation of parallel computers; this enhanced version delivers practical and competitive performance with the parallel computers of today.

Copyright © 2009 by American Society of Mechanical Engineers
Topics: Algorithms , Equations , Chain
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Figure 1

Example of a chain system

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Figure 2

Example of a binary assembly tree

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Figure 3

DCA performance (1024 body chain)

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Figure 4

O(n) terminal subsystems (1024 body chain)

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Figure 5

Efficient DCA (1024 body chain)

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Figure 6

Efficient DCA with few processors (1024 body chain)

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Figure 7

Load balancing results

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Figure 8

Algorithm timing results




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