A New Algorithm of Proper Generalized Decomposition for Parametric Symmetric Elliptic Problems
| dc.contributor.author | AZAÏEZ, M. | |
| hal.structure.identifier | Laboratoire de Mathématiques Appliquées de Compiègne [LMAC] | |
| dc.contributor.author | BELGACEM, F. Ben | |
| dc.contributor.author | CASADO-DÍAZ, J. | |
| dc.contributor.author | REBOLLO, T. Chacón | |
| hal.structure.identifier | Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)] | |
| dc.contributor.author | MURAT, F. | |
| dc.date.accessioned | 2021-05-14T09:45:25Z | |
| dc.date.available | 2021-05-14T09:45:25Z | |
| dc.date.issued | 2018-01 | |
| dc.identifier.issn | 0036-1410 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/76933 | |
| dc.description.abstractEn | We introduce a new algorithm of proper generalized decomposition (PGD) for parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension which realizes the best approximation---in the mean parametric norm associated to the elliptic operator---of the error between the exact solution and the Galerkin solution calculated on the subspace. This is analogous to the best approximation property of the proper orthogonal decomposition (POD) subspaces, except that in our case the norm is parameter-dependent. We apply a deflation technique to build a series of approximating solutions on finite-dimensional optimal subspaces, directly in the online step, and we prove that the partial sums converge to the continuous solution in the mean parametric elliptic norm. We show that the standard PGD for the considered parametric problem is strongly related to the deflation algorithm introduced in this paper. This opens the possibility of computing the PGD expansion by directly solving the optimization problems that yield the optimal subspaces. | |
| dc.language.iso | en | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.title.en | A New Algorithm of Proper Generalized Decomposition for Parametric Symmetric Elliptic Problems | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math] | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| bordeaux.journal | SIAM Journal on Mathematical Analysis | |
| bordeaux.page | 5426-5445 | |
| bordeaux.volume | 50 | |
| bordeaux.hal.laboratories | Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295 | * |
| bordeaux.issue | 5 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.institution | INRAE | |
| bordeaux.institution | Arts et Métiers | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01939854 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01939854v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Mathematical%20Analysis&rft.date=2018-01&rft.volume=50&rft.issue=5&rft.spage=5426-5445&rft.epage=5426-5445&rft.eissn=0036-1410&rft.issn=0036-1410&rft.au=AZA%C3%8FEZ,%20M.&BELGACEM,%20F.%20Ben&CASADO-D%C3%8DAZ,%20J.&REBOLLO,%20T.%20Chac%C3%B3n&MURAT,%20F.&rft.genre=article |
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