Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations

Kevin Carlberg, Charbel Bou-Mosleh, Charbel Farhat

Research output: Contribution to journalArticlepeer-review

313 Scopus citations

Abstract

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. © 2010 John Wiley & Sons, Ltd.
Original languageEnglish (US)
Pages (from-to)155-181
Number of pages27
JournalInternational Journal for Numerical Methods in Engineering
Volume86
Issue number2
DOIs
StatePublished - Oct 28 2010
Externally publishedYes

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