An adaptive model order reduction with Quasi-Newton method for nonlinear dynamical problems

authored by: P. S.B. Nigro, M. Anndif, Y. Teixeira, P. M. Pimenta, P. Wriggers
Abstract: Model Order Reduction (MOR) methods are extremely useful to reduce processing time, even nowadays, when parallel processing is possible in any personal computer. This work describes a method that combines Proper Orthogonal Decomposition (POD) and Ritz vectors to achieve an efficient Galerkin projection, which changes during nonlinear solving (online analysis). It is supported by a new adaptive strategy, which analyzes the error and the convergence rate for nonlinear dynamical problems. This model order reduction is assisted by a secant formulation which is updated by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula to accelerate convergence in the reduced space, and a tangent formulation when correction of the reduced space is needed. Furthermore, this research shows that this adaptive strategy permits correction of the reduced model at low cost and small error.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Universidade de Sao Paulo
Type: Article
Journal: International Journal for Numerical Methods in Engineering
Volume: 106
Pages: 740-759
No. of pages: 20
ISSN: 0029-5981
Publication date: 19.10.2015
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, General Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.1002/nme.5145 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{259887c1acd0424f8ef892f7286d1aa4,
title = "An adaptive model order reduction with Quasi-Newton method for nonlinear dynamical problems",
abstract = "Model Order Reduction (MOR) methods are extremely useful to reduce processing time, even nowadays, when parallel processing is possible in any personal computer. This work describes a method that combines Proper Orthogonal Decomposition (POD) and Ritz vectors to achieve an efficient Galerkin projection, which changes during nonlinear solving (online analysis). It is supported by a new adaptive strategy, which analyzes the error and the convergence rate for nonlinear dynamical problems. This model order reduction is assisted by a secant formulation which is updated by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula to accelerate convergence in the reduced space, and a tangent formulation when correction of the reduced space is needed. Furthermore, this research shows that this adaptive strategy permits correction of the reduced model at low cost and small error.",
keywords = "Adaptive strategy, BFGS, Galerkin projection, Model order reduction, Nonlinear dynamic analysis, POD",
author = "Nigro, {P. S.B.} and M. Anndif and Y. Teixeira and Pimenta, {P. M.} and P. Wriggers",
year = "2015",
month = oct,
day = "19",
doi = "10.1002/nme.5145",
language = "English",
volume = "106",
pages = "740--759",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "9",
}