An adaptive model order reduction by proper snapshot selection 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 employed in many fields of Engineering in order to reduce the processing time of complex computational simulations. A usual approach to achieve this is the application of Galerkin projection to generate representative subspaces (reduced spaces). However, when strong nonlinearities in a dynamical system are present and this technique is employed several times along the simulation, it can be very inefficient. This work proposes a new adaptive strategy, which ensures low computational cost and small error to deal with this problem. This work also presents a new method to select snapshots named Proper Snapshot Selection (PSS). The objective of the PSS is to obtain a good balance between accuracy and computational cost by improving the adaptive strategy through a better snapshot selection in real time (online analysis). With this method, it is possible a substantial reduction of the subspace, keeping the quality of the model without the use of the Proper Orthogonal Decomposition (POD).
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Universidade de Sao Paulo
Type: Article
Journal: Computational mechanics
Volume: 57
Pages: 537-554
No. of pages: 18
ISSN: 0178-7675
Publication date: 04.2016
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-015-1238-y (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{a6c907a383bd4f7686a48db283b4bd0e,
title = "An adaptive model order reduction by proper snapshot selection for nonlinear dynamical problems",
abstract = "Model Order Reduction (MOR) methods are employed in many fields of Engineering in order to reduce the processing time of complex computational simulations. A usual approach to achieve this is the application of Galerkin projection to generate representative subspaces (reduced spaces). However, when strong nonlinearities in a dynamical system are present and this technique is employed several times along the simulation, it can be very inefficient. This work proposes a new adaptive strategy, which ensures low computational cost and small error to deal with this problem. This work also presents a new method to select snapshots named Proper Snapshot Selection (PSS). The objective of the PSS is to obtain a good balance between accuracy and computational cost by improving the adaptive strategy through a better snapshot selection in real time (online analysis). With this method, it is possible a substantial reduction of the subspace, keeping the quality of the model without the use of the Proper Orthogonal Decomposition (POD).",
keywords = "Adaptive strategy, Galerkin projection, Model order reduction, Nonlinear dynamic analysis, PSS, Ritz vector",
author = "Nigro, {P. S.B.} and M. Anndif and Y. Teixeira and Pimenta, {P. M.} and P. Wriggers",
note = "Funding Information: The fourth author acknowledges the support by CNPq (Conselho Nacional de Desenvolvimento Cient{\'i}fico e Tecnol{\'o}gico) under the grant 303091/2013-4 as well as expresses his gratitude to the Alexander von Humboldt Foundation for the Georg Forster Research Award that made possible his stay at the University of Duisburg-Essen and the Leibniz University of Hannover. Funding Information: The first author acknowledges the support by CNPq (Conselho Nacional de Desenvolvimento Cient{\'i}fico e Tecnol{\'o}gico) under the grant 201656/2012-4 that made possible his stay at the Leibniz University of Hannover.",
year = "2016",
month = apr,
doi = "10.1007/s00466-015-1238-y",
language = "English",
volume = "57",
pages = "537--554",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "4",
}