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Multiscale proper generalized decomposition based on the partition of unity

Article dans une revue avec comité de lecture
Author
IBÁÑEZ PINILLO, Rubén
ccCUETO, Elias
95355 Universidad de Zaragoza = University of Zaragoza [Saragossa University] = Université de Saragosse
HUERTA, Antonio
85878 Universitat Politècnica de Catalunya = Université polytechnique de Catalogne [Barcelona] [UPC]
DUVAL, Jean-Louis
564849 ESI Group [ESI Group]
ccAMMAR, Amine
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
ccCHINESTA SORIA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]

URI
http://hdl.handle.net/10985/18456
DOI
10.1002/nme.6154
Date
2019
Journal
International Journal for Numerical Methods in Engineering

Abstract

Solutions of partial differential equations could exhibit a multiscale behavior. Standard discretization techniques are constraints to mesh up to the finest scale to predict accurately the response of the system. The proposed methodology is based on the standard proper generalized decomposition rationale; thus, the PDE is transformed into a nonlinear system that iterates between microscale and macroscale states, where the time coordinate could be viewed as a 2D time, representing the microtime and macrotime scales. The macroscale effects are taken into account because of an FEM-based macrodiscretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the domain. The proposed methodology can be seen as an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors.

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