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 hal.structure.identifier
CHINESTA, Francisco
10921 Institut de Recherche en Génie Civil et Mécanique [GeM]
dc.contributor.author
 hal.structure.identifier
AMMAR, Amine
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
dc.contributor.author
 hal.structure.identifier
LEYGUE, Adrien
10921 Institut de Recherche en Génie Civil et Mécanique [GeM]
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KEUNINGS, Roland
92863 Université Catholique de Louvain = Catholic University of Louvain [UCL]
dc.date.accessioned2014
dc.date.available2014
dc.date.issued2011
dc.date.submitted2014
dc.identifier.issn0377-0257
dc.identifier.urihttp://hdl.handle.net/10985/8473
dc.description.abstractWe 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.
dc.language.isoen_US
dc.publisherElsevier
dc.rightsPost-print
dc.subjectComplex fluids
dc.subjectNumerical modeling
dc.subjectModel reduction
dc.subjectProper orthogonal decomposition
dc.subjectProper generalized decomposition
dc.subjectKinetic theory
dc.subjectParametric models
dc.subjectOptimization
dc.subjectInverse identification
dc.titleAn overview of the proper generalized decomposition with applications in computational rheology
dc.identifier.doi10.1016/j.jnnfm.2010.12.012
dc.typdocArticle dans une revue avec comité de lecture
dc.localisationCentre de Angers
dc.subject.halSciences de l'ingénieur: Mécanique: Mécanique des fluides
ensam.audienceInternationale
ensam.page578-592
ensam.journalJournal of Non-Newtonian Fluid Mechanics
ensam.volume166
ensam.issue11
hal.identifierhal-01061441
hal.version1
hal.submission.permittedupdateMetadata
hal.statusaccept


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