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Wavelet-based multiscale proper generalized decomposition

Article dans une revue avec comité de lecture
Author
ANGEL, Leon
111023 École Centrale de Nantes [ECN]
BARASINSKI, Anais
10921 Institut de Recherche en Génie Civil et Mécanique [GeM]
ABISSET-CHAVANNE, Emmanuelle
111023 École Centrale de Nantes [ECN]
CUETO, Elias
95355 University of Zaragoza - Universidad de Zaragoza [Zaragoza]
CHINESTA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]

URI
http://hdl.handle.net/10985/13282
DOI
10.1016/j.crme.2018.04.013
Date
2018
Journal
Comptes Rendus Mécanique

Abstract

Separated representations at the heart of Proper Generalized Decomposition are constructed incrementally by minimizing the problem residual. However, the modes involved in the resulting decomposition do not exhibit a clear multi-scale character. In order to recover a multi-scale description of the solution within a separated representation framework, we study the use of wavelets for approximating the functions involved in the separated representation of the solution. We will prove that such an approach allows separating the different scales as well as taking profit from its multi-resolution behavior for defining adaptive strategies.

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