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

Type
Articles dans des revues avec comité de lecture
Auteur
IBAÑEZ, Ruben
111023 École Centrale de Nantes [ECN]
445111 Institut de Calcul Intensif [ICI]
ABISSET-CHAVANNE, Emmanuelle
111023 École Centrale de Nantes [ECN]
445111 Institut de Calcul Intensif [ICI]
CHINESTA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
HUERTA, Antonio
81618 Laboratori de Càlcul Numèric (LACAN) [LaCàN]
CUETO, Elías G.
95355 University of Zaragoza - Universidad de Zaragoza [Zaragoza]

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

Résumé

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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Documents liés

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  • A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition 
    IBAÑEZ, Rubén; ABISSET-CHAVANNE, Emmanuelle; AMMAR, Amine; GONZALEZ, David; CUETO, Elias; HUERTA, Antonio; DUVAL, Jean Louis; CHINESTA, Francisco (Hindawi Limited, 2018)
    Sparse model identification by means of data is especially cumbersome if the sought dynamics live in a high dimensional space. This usually involves the need for large amount of data, unfeasible in such a high dimensional ...
  • Radars in Transport Applications 
    IBÁÑEZ PINILLO, Rubén; CHINESTA, Francisco; ABISSET-CHAVANNE, Emmanuelle; ABENIUS, Erik; HUERTA, Antonio (Springer, 2020)
    In the recent years, automotive car industry is evolving towards a new generation of autonomous vehicles, where decision making is not fully perform by the driver but it partially relies on the technology of the car itself. ...
  • A simple microstructural viscoelastic model for flowing foams 
    IBÁÑEZ, Rubén; SCHEUER, Adrien; ABISSET-CHAVANNE, Emmanuelle; CHINESTA, Francisco; HUERTA, Antonio; KEUNINGS, Roland (Springer-Verlag France, 2018)
    The numerical modelling of forming processes involving the flow of foams requires taking into account the different problem scales. Thus, in industrial applications a macroscopic approach is suitable, whereas the macroscopic ...
  • Hybrid constitutive modeling: data-driven learning of corrections to plasticity models 
    IBÁÑEZ, Rubén; ABISSET-CHAVANNE, Emmanuelle; GONZÁLEZ, David; DUVAL, Jean Louis; CUETO, Elias; CHINESTA, Francisco (Springer-Verlag France, 2019)
    In recent times a growing interest has arose on the development of data-driven techniques to avoid the employ of phenomenological constitutive models. While it is true that, in general, data do not fit perfectly to existing ...
  • Some applications of compressed sensing in computational mechanics: model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction 
    IBAÑEZ, R.; ABISSET-CHAVANNE, Emmanuelle; CUETO, Elías G.; AMMAR, Amine; DUVAL, Jean Louis; CHINESTA, Francisco (Springer, 2019)
    Compressed sensing is a signal compression technique with very remarkable properties. Among them, maybe the most salient one is its ability of overcoming the Shannon–Nyquist sampling theorem. In other words, it is able to ...

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