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Recent Advances in the Use of Separated Representations

hal.structure.identifierAragón Institute of Engineering Research [Zaragoza] [I3A]
dc.contributor.authorGONZALEZ, David
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.authorCHINESTA, Francisco
hal.structure.identifierAragón Institute of Engineering Research [Zaragoza] [I3A]
dc.contributor.authorCUETO, Elías
dc.date.accessioned2021-05-14T09:52:14Z
dc.date.available2021-05-14T09:52:14Z
dc.date.issued2010
dc.identifier.issn0029-5981
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/77433
dc.description.abstractEnSeparated representations based on finite sum decompositions constitute an appealing strategy for reducing the computer resources and the calculation costs by reducing drastically the number of degrees of freedom that the functional approximations involve (the number of degrees of freedom scale linearly with the dimension of the space in which the model is defined instead of the exponential growing characteristic of mesh-based discretization strategies). In our knowledge the use of separated representations is the only possibility for circumventing the terrific curse of dimensionality related to some highly multidimensional models involving hundreds of dimensions, as we proved in some of our former works. Its application is not restricted to multidimensional models, obviously separated representation can also be applied in standard 2D or 3D models, allowing for high resolution computations. Because its early life numerous issues persist, many of them attracting the Curiosity of many research groups within the computational mechanics community. In this paper we are focusing in two issues never until now addressed: (i) the imposition of non-homogenous essential boundary conditions and (ii) the consideration of complex geometries.
dc.language.isoen
dc.publisherWiley
dc.rights.urihttp://creativecommons.org/licenses/by/
dc.subject.enseparation of variables
dc.subject.encurse of dimensionality
dc.subject.ensingular value decomposition
dc.subject.enessential boundary conditions
dc.title.enRecent Advances in the Use of Separated Representations
dc.typeArticle de revue
dc.identifier.doi10.1002/nme.2710
dc.subject.halSciences de l'ingénieur [physics]/Mécanique [physics.med-ph]
dc.subject.halSciences de l'ingénieur [physics]/Matériaux
bordeaux.journalInternational Journal for Numerical Methods in Engineering
bordeaux.page637-659
bordeaux.volume81
bordeaux.hal.laboratoriesInstitut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295*
bordeaux.issue5
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.institutionINRAE
bordeaux.institutionArts et Métiers
bordeaux.peerReviewedoui
hal.identifierhal-01007237
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01007237v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=International%20Journal%20for%20Numerical%20Methods%20in%20Engineering&rft.date=2010&rft.volume=81&rft.issue=5&rft.spage=637-659&rft.epage=637-659&rft.eissn=0029-5981&rft.issn=0029-5981&rft.au=GONZALEZ,%20David&AMMAR,%20Amine&CHINESTA,%20Francisco&CUETO,%20El%C3%ADas&rft.genre=article


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