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A local multiple proper generalized decomposition based on the partition of unity

Article dans une revue avec comité de lecture
Author
IBAÑEZ, Ruben
HUERTA, Antonio
81618 Laboratori de Càlcul Numèric (LACAN) [LaCàN]
ccCUETO, Elias
95355 Universidad de Zaragoza = University of Zaragoza [Saragossa University] = Université de Saragosse
ccABISSET-CHAVANNE, Emmanuelle
111023 École Centrale de Nantes [ECN]
445111 Institut de Calcul Intensif [ICI]
ccCHINESTA SORIA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]

URI
http://hdl.handle.net/10985/17949
DOI
10.1002/nme.6128
Date
2019
Journal
International Journal for Numerical Methods in Engineering

Abstract

It is well known that model order reduction techniques that project the solution of the problem at hand onto a low-dimensional subspace present difficulties when this solution lies on a nonlinear manifold. To overcome these difficulties (notably, an undesirable increase in the number of required modes in the solution), several solutions have been suggested. Among them, we can cite the use of nonlinear dimensionality reduction techniques or, alternatively, the employ of linear local reduced order approaches. These last approaches usually present the difficulty of ensuring continuity between these local models. Here, a new method is presented, which ensures this continuity by resorting to the paradigm of the partition of unity while employing proper generalized decompositions at each local patch.

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