Multiscale proper generalized decomposition based on the partition of unity

Rubén Ibáñez Pinillo (1) , Amine Ammar (2) , Elías G. Cueto (3) , Antonio Huerta (4) , Jean Louis Duval (5) , Francisco Chinesta (1)

1 PIMM - Laboratoire Procédés et Ingénierie en Mécanique et Matériaux
2 LAMPA - Laboratoire Angevin de Mécanique, Procédés et InnovAtion
3 University of Zaragoza - Universidad de Zaragoza [Zaragoza]
4 UPC - Universitat Politècnica de Catalunya = Université polytechnique de Catalogne [Barcelona]
5 ESI Group - ESI Group

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.

Mots clés: time multiscale; proper generalized decomposition; partition of unity

Domaines: Matériaux

Rubén Ibáñez Pinillo, Amine Ammar, Elías G. Cueto, Antonio Huerta, Jean Louis Duval, et al.. Multiscale proper generalized decomposition based on the partition of unity. International Journal for Numerical Methods in Engineering, 2019, 120 (6), pp.727-747. ⟨10.1002/nme.6154⟩. ⟨hal-02545484⟩