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

hal.structure.identifierInstitut de Recherche en Génie Civil et Mécanique [GeM]
dc.contributor.authorCHINESTA, Francisco
hal.structure.identifierLaboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
dc.contributor.authorAMMAR, Amine
hal.structure.identifierInstitut de Recherche en Génie Civil et Mécanique [GeM]
dc.contributor.authorLEYGUE, Adrien
hal.structure.identifierUniversité Catholique de Louvain = Catholic University of Louvain [UCL]
dc.contributor.authorKEUNINGS, Roland
dc.date.accessioned2021-05-14T10:00:25Z
dc.date.available2021-05-14T10:00:25Z
dc.date.issued2011-06
dc.identifier.issn0377-0257
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/78128
dc.description.abstractEnWe 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
dc.publisherElsevier
dc.subject.enComplex fluids
dc.subject.enNumerical modeling
dc.subject.enModel reduction
dc.subject.enProper orthogonal decomposition
dc.subject.enProper generalized decomposition
dc.subject.enKinetic theory
dc.subject.enParametric models
dc.subject.enOptimization
dc.subject.enInverse identification
dc.title.enAn overview of the proper generalized decomposition with applications in computational rheology
dc.typeArticle de revue
dc.subject.halSciences de l'ingénieur [physics]/Mécanique [physics.med-ph]/Mécanique des fluides [physics.class-ph]
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
bordeaux.journalJournal of Non-Newtonian Fluid Mechanics
bordeaux.page578-592
bordeaux.volume166
bordeaux.hal.laboratoriesInstitut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295*
bordeaux.issue11
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.institutionINRAE
bordeaux.institutionArts et Métiers
bordeaux.peerReviewedoui
hal.identifierhal-01061441
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01061441v1
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