This paper sets out to demonstrate three things: (i) implicit integration with absolute nodal coordinate formulation (ANCF) is effective in handling very stiff systems when an accurate computation of the sensitivity matrix is part of the solution sequence, (ii) parallel computing can provide a vehicle for ANCF to tackle very large kinematically constrained problems with millions of degrees of freedom and produce results in a matter of seconds, and (iii) large systems of equations associated with implicit integration can be solved in parallel by relying on an iterative approach that avoids costly matrix factorizations, which would be prohibitively expensive and memory intensive. For (iii), the approach adopted relies on a Krylov–subspace method that is invoked in the Newton stage at each time step of the numerical solution process. The proposed approach is validated against a commercial package and several simple systems for which analytical solutions are available. A set of numerical experiments demonstrates the scaling of the parallel solution method and provides insights in relation to the size of ANCF problems that are tractable using graphics processing unit (GPU) parallel computing and implicit numerical integration.
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Warren, MI 48397
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January 2014
Research-Article
A Matrix-Free Newton–Krylov Parallel Implicit Implementation of the Absolute Nodal Coordinate Formulation
Daniel Melanz,
1513 University Avenue,
Daniel Melanz
Department of Mechanical Engineering
,1513 University Avenue,
Madison, WI 53706
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Naresh Khude,
1513 University Avenue,
Naresh Khude
Department of Mechanical Engineering
,1513 University Avenue,
Madison, WI 53706
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Paramsothy Jayakumar,
Development and Engineering Center,
Warren, MI 48397
Paramsothy Jayakumar
U.S. Army Tank Automotive Research
,Development and Engineering Center,
6501 East 11 Mile Road
,Warren, MI 48397
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Dan Negrut
1513 University Avenue,
Dan Negrut
Department of Mechanical Engineering
,1513 University Avenue,
Madison, WI 53706
Search for other works by this author on:
Daniel Melanz
Department of Mechanical Engineering
,1513 University Avenue,
Madison, WI 53706
Naresh Khude
Department of Mechanical Engineering
,1513 University Avenue,
Madison, WI 53706
Paramsothy Jayakumar
U.S. Army Tank Automotive Research
,Development and Engineering Center,
6501 East 11 Mile Road
,Warren, MI 48397
Dan Negrut
Department of Mechanical Engineering
,1513 University Avenue,
Madison, WI 53706
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 3, 2012; final manuscript received May 1, 2013; published online October 9, 2013. Assoc. Editor: Hiroyuki Sugiyama.
J. Comput. Nonlinear Dynam. Jan 2014, 9(1): 011006 (9 pages)
Published Online: October 9, 2013
Article history
Received:
December 3, 2012
Revision Received:
May 1, 2013
Citation
Melanz, D., Khude, N., Jayakumar, P., and Negrut, D. (October 9, 2013). "A Matrix-Free Newton–Krylov Parallel Implicit Implementation of the Absolute Nodal Coordinate Formulation." ASME. J. Comput. Nonlinear Dynam. January 2014; 9(1): 011006. https://doi.org/10.1115/1.4025281
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