CHINESTA, Francisco; AMMAR, Amine; LEYGUE, Adrien; KEUNINGS, Roland

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CHINESTA, Francisco
Institut de Recherche en Génie Civil et Mécanique [GeM]

AMMAR, Amine
Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]

LEYGUE, Adrien
Institut de Recherche en Génie Civil et Mécanique [GeM]

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Ce document a été publié dans

Journal of Non-Newtonian Fluid Mechanics. 2011-06, vol. 166, n° 11, p. 578-592

Elsevier

Résumé en anglais

We review the foundations and applications of the proper generalized decomposition (PGD), a powerful model reduction technique that computes a priori by means of successive enrichment a separated representation of the unknown field. The computational complexity of the PGD scales linearly with the dimension of the space wherein the model is defined, which is in marked contrast with the exponential scaling of standard grid-based methods. First introduced in the context of computational rheology by Ammar et al. [3] and [4], the PGD has since been further developed and applied in a variety of applications ranging from the solution of the Schrödinger equation of quantum mechanics to the analysis of laminate composites. In this paper, we illustrate the use of the PGD in four problem categories related to computational rheology: (i) the direct solution of the Fokker-Planck equation for complex fluids in configuration spaces of high dimension, (ii) the development of very efficient non-incremental algorithms for transient problems, (iii) the fully three-dimensional solution of problems defined in degenerate plate or shell-like domains often encountered in polymer processing or composites manufacturing, and finally (iv) the solution of multidimensional parametric models obtained by introducing various sources of problem variability as additional coordinates.< Réduire

Mots clés en anglais

Complex fluids

Numerical modeling

Model reduction

Proper orthogonal decomposition

Proper generalized decomposition

Kinetic theory

Parametric models

Optimization

Inverse identification

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An overview of the proper generalized decomposition with applications in computational rheology

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Mots clés en anglais

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