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Abstract
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| Automatic differentiation is a very powerful computational-mathematical technique that is capable of differentiating any type of computer function. Among its advantages over other ways of computing derivatives, the most important are accuracy, scalability, efficiency and short development time. This article is about the implementation of automatic differentiation in a recursive penalty formulation for the dynamic simulation of multibody systems. Specifically, the technique is implemented in the most expensive step of the formulation: the differentiation of a set of forces in the form of a Jacobian matrix. Both the details of the formulation and the basics of automatic differentiation appear here thoroughly explained. The numerical examples at the end prove that automatic differentiation overcomes some of the limitations of numerical differentiation, and they offer interesting information about the influence of the problem size in the efficiency of the simulation. In some examples, the speedup of automatic differentiation with respect to numerical differentiation reaches 64%. Summing up, this paper provides an original perspective for the optimization of derivatives in the context of efficient multibody formulations. | |
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International
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Si |
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Congress
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ECCOMAS Multibody Dynamics 2011, J.C. Samin, P. Fisette (eds.), Brussels, July 4-7, 2011. |
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960 |
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Place
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Reviewers
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Si |
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ISBN/ISSN
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978-2-8052-0116-5 |
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Start Date
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04/07/2011 |
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End Date
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07/07/2011 |
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From page
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1 |
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To page
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10 |
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ECCOMAS Multibody Dynamics 2011, J.C. Samin, P. Fisette (eds.), |