000109705 001__ 109705
000109705 005__ 20220908120605.0
000109705 0247_ $$2doi$$a10.1186/s40323-021-00211-7
000109705 0248_ $$2sideral$$a126771
000109705 037__ $$aART-2021-126771
000109705 041__ $$aeng
000109705 100__ $$aPasquale A.
000109705 245__ $$aA separated representation involving multiple time scales within the Proper Generalized Decomposition framework
000109705 260__ $$c2021
000109705 5060_ $$aAccess copy available to the general public$$fUnrestricted
000109705 5203_ $$aSolutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems. © 2021, The Author(s).
000109705 536__ $$9info:eu-repo/grantAgreement/ES/MINECO-CICYT/DPI2017-85139-C2-1-R
000109705 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000109705 592__ $$a0.877$$b2021
000109705 594__ $$a4.1$$b2021
000109705 593__ $$aApplied Mathematics$$c2021$$dQ1
000109705 593__ $$aEngineering (miscellaneous)$$c2021$$dQ1
000109705 593__ $$aComputer Science Applications$$c2021$$dQ1
000109705 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000109705 700__ $$aAmmar A.
000109705 700__ $$aFalcó A.
000109705 700__ $$aPerotto S.
000109705 700__ $$0(orcid)0000-0003-1017-4381$$aCueto E.$$uUniversidad de Zaragoza
000109705 700__ $$aDuval J.-L.
000109705 700__ $$aChinesta F.
000109705 7102_ $$15004$$2605$$aUniversidad de Zaragoza$$bDpto. Ingeniería Mecánica$$cÁrea Mec.Med.Cont. y Teor.Est.
000109705 773__ $$g8, 1 (2021), 26 [22 pp]$$pAdv. model. simul. eng. sci.$$tAdvanced modeling and simulation in engineering sciences$$x2213-7467
000109705 8564_ $$s1587451$$uhttps://zaguan.unizar.es/record/109705/files/texto_completo.pdf$$yVersión publicada
000109705 8564_ $$s2148252$$uhttps://zaguan.unizar.es/record/109705/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000109705 909CO $$ooai:zaguan.unizar.es:109705$$particulos$$pdriver
000109705 951__ $$a2022-09-08-11:58:11
000109705 980__ $$aARTICLE