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dc.contributor.authorPRULIERE, Etienne
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
dc.date.accessioned2021-05-14T10:04:38Z
dc.date.available2021-05-14T10:04:38Z
dc.date.issued2010-12
dc.identifier.issn0378-4754
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/78503
dc.description.abstractEnThis paper focuses on the efficient solution of models defined in high dimensional spaces. Those models involve numerous numerical challenges because of their associated curse of dimensionality. It is well known that in meshbased discrete models the complexity (degrees of freedom) scales exponentially with the dimension of the space. Many models encountered in computational science and engineering involve numerous dimensions called configurational coordinates. Some examples are the models encountered in biology making use of the chemical master equation, quantum chemistry involving the solution of the Schr¨odinger or Dirac equations, kinetic theory descriptions of complex systems based on the solution of the so-called Fokker-Planck equation, stochastic models in which the random variables are included as new coordinates, financial mathematics, ... This paper revisits the curse of dimensionality and proposes an efficient strategy for circumventing such challenging issue. This strategy, based on the use of a Proper Generalized Decomposition, is specially well suited to treat the multidimensional parametric equations.
dc.language.isoen
dc.publisherElsevier
dc.subject.enMultidimensional models
dc.subject.enCurse of dimensionality
dc.subject.enParametric models
dc.subject.enProper Generalized Decompositions
dc.subject.enSeparated representations
dc.title.enOn the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition
dc.typeArticle de revue
dc.identifier.doi10.1016/j.matcom.2010.07.015
dc.subject.halInformatique [cs]/Intelligence artificielle [cs.AI]
dc.subject.halSciences de l'ingénieur [physics]/Mécanique [physics.med-ph]
bordeaux.journalMathematics and Computers in Simulation
bordeaux.page791-810
bordeaux.volume81
bordeaux.hal.laboratoriesInstitut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.institutionINRAE
bordeaux.institutionArts et Métiers
bordeaux.peerReviewedoui
hal.identifierhal-00704427
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00704427v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematics%20and%20Computers%20in%20Simulation&rft.date=2010-12&rft.volume=81&rft.issue=4&rft.spage=791-810&rft.epage=791-810&rft.eissn=0378-4754&rft.issn=0378-4754&rft.au=PRULIERE,%20Etienne&CHINESTA,%20Francisco&AMMAR,%20Amine&rft.genre=article


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