期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
卷 86, 期 2, 页码 155-181出版社
WILEY
DOI: 10.1002/nme.3050
关键词
non-linear model reduction; compressive approximation; discrete non-linear systems; gappy data; Petrov-Galerkin projection; proper orthogonal decomposition
资金
- National Science Foundation
- National Defense Science and Engineering
- Motor Sports Division of the Toyota Motor Corporation [48737]
- King Abdullah University of Science and Technology (KAUST)
- Stanford University
A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. Copyright (C) 2010 John Wiley & Sons, Ltd.
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