000057887 001__ 57887
000057887 005__ 20170327111938.0
000057887 0247_ $$2doi$$a10.1186/s40323-015-0052-6
000057887 0248_ $$2sideral$$a96918
000057887 037__ $$aART-2015-96918
000057887 041__ $$aeng
000057887 100__ $$aZlotnik, Sergio
000057887 245__ $$aEffect of the separated approximation of input data in the accuracy of the resulting PGD solution
000057887 260__ $$c2015
000057887 5060_ $$aAccess copy available to the general public$$fUnrestricted
000057887 5203_ $$aThe proper generalized decomposition (PGD) requires separability of the input data (e.g. physical properties, source term, boundary conditions, initial state). In many cases the input data is not expressed in a separated form and it has to be replaced by some separable approximation. These approximations constitute a new error source that, in some cases, may dominate the standard ones (discretization, truncation...) and control the final accuracy of the PGD solution. In this work the relation between errors in the separated input data and the errors induced in the PGD solution is discussed. Error estimators proposed for homogenized problems and oscillation terms are adapted to asses the behaviour of the PGD errors resulting from approximated input data. The PGD is stable with respect to error in the separated data, with no critical amplification of the perturbations. Interestingly, we identified a high sensitiveness of the resulting accuracy on the selection of the sampling grid used to compute the separated data. The separation has to be performed on the basis of values sampled at integration points: sampling at the nodes defining the functional interpolation results in an important loss of accuracy. For the case of a Poisson problem separated in the spatial coordinates (a complex diffusivity function requires a separable approximation), the final PGD error is linear with the truncation error of the separated data. This relation is used to estimate the number of terms required in the separated data, that has to be in good agreement with the truncation error accepted in the PGD truncation (tolerance for the stoping criteria in the enrichment procedure). A sensible choice for the prescribed accuracy of the PGD solution has to be kept within the limits set by the errors in the separated input data.
000057887 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/DPI2014-51844-C2-1-2-R
000057887 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000057887 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000057887 700__ $$aDíez, Pedro
000057887 700__ $$0(orcid)0000-0003-3003-5856$$aGonzalez, David$$uUniversidad de Zaragoza
000057887 700__ $$aCueto, Elías
000057887 700__ $$aHuerta, Antonio
000057887 7102_ $$15004$$2605$$aUniversidad de Zaragoza$$bDepartamento de Ingeniería Mecánica$$cMec. de Medios Contínuos y Teor. de Estructuras
000057887 773__ $$g2, 28 (2015), [14 pp.]$$pAdv. model. simul. eng. sci.$$tAdvanced modeling and simulation in engineering sciences$$x2213-7467
000057887 8564_ $$s2285638$$uhttps://zaguan.unizar.es/record/57887/files/texto_completo.pdf$$yVersión publicada
000057887 8564_ $$s16944$$uhttps://zaguan.unizar.es/record/57887/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000057887 909CO $$ooai:zaguan.unizar.es:57887$$particulos$$pdriver
000057887 951__ $$a2016-12-15-15:03:38
000057887 980__ $$aARTICLE