Multiscale Proper Generalized Decomposition based on the Partition of Unity

Author (s): Ibanez, R., Ammar, A., Cueto, E., Huerta, A., Duval, J.-L., and Chinesta, F.
Journal: International Journal for Numerical Methods in Engineering

Volume: 120, Issue 6
Pages: 727 – 747
Date: 2019

Abstract:
Solutions of partial differential equations could exhibit a multi-scale behavior. Standard discretization techniques are constraint to mesh up to the finest scale in order to predict accurately the response of the system. The proposed methodology projects the solution of the PDE into a set of parent unidimensional spaces which are solved following the standard PGD rationale. The proposed methodology can be seen as an alternative to circumvent prohibitive meshes arising from the necessity of capturing fine scale features.

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Bibtex:

@article {PC-IACHDC:19,
        Author = {Ruben Ibanez and Amine Ammar and Elias Cueto and Antonio Huerta and Jean-Louis Duval and Francisco Chinesta},
        Title = {Multiscale Proper Generalized Decomposition based on the Partition of Unity},
        Fjournal = {International Journal for Numerical Methods in Engineering},
        Journal = {Int. J. Numer. Methods Eng.},
        Volume = {120},
        Number = {6},
        Pages = {727--747},
        Year = {2019}
        }