Comptes Rendus
Model reduction, data-based and advanced discretization in computational mechanics
Wavelet-based multiscale proper generalized decomposition
Comptes Rendus. Mécanique, Volume 346 (2018) no. 7, pp. 485-500.

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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Accepted:
Published online:
DOI: 10.1016/j.crme.2018.04.013
Keywords: Wavelets, Proper Generalized Decomposition, Multi-resolution, Multi-scale PGD

Angel Leon 1; Anais Barasinski 1; Emmanuelle Abisset-Chavanne 2; Elias Cueto 3; Francisco Chinesta 4

1 GeM Institute, École centrale de Nantes, 1, rue de la Noë, BP 92101, 44321 Nantes cedex 3, France
2 High Performance Computing Institute & ESI GROUP Chair, École centrale de Nantes, 1, rue de la Noë, BP 92101, 44321 Nantes cedex 3, France
3 I3A, University of Zaragoza, Maria de Luna s/n, 50018 Zaragoza, Spain
4 PIMM Laboratory & ESI GROUP Chair, ENSAM ParisTech, 151, boulevard de l'Hôpital, 75013 Paris, France
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Angel Leon; Anais Barasinski; Emmanuelle Abisset-Chavanne; Elias Cueto; Francisco Chinesta. Wavelet-based multiscale proper generalized decomposition. Comptes Rendus. Mécanique, Volume 346 (2018) no. 7, pp. 485-500. doi : 10.1016/j.crme.2018.04.013. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.04.013/

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