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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Angel Leon 1 ; Anais Barasinski 1 ; Emmanuelle Abisset-Chavanne 2 ; Elias Cueto 3 ; Francisco Chinesta 4
@article{CRMECA_2018__346_7_485_0,
author = {Angel Leon and Anais Barasinski and Emmanuelle Abisset-Chavanne and Elias Cueto and Francisco Chinesta},
title = {Wavelet-based multiscale proper generalized decomposition},
journal = {Comptes Rendus. M\'ecanique},
pages = {485--500},
publisher = {Elsevier},
volume = {346},
number = {7},
year = {2018},
doi = {10.1016/j.crme.2018.04.013},
language = {en},
}
TY - JOUR AU - Angel Leon AU - Anais Barasinski AU - Emmanuelle Abisset-Chavanne AU - Elias Cueto AU - Francisco Chinesta TI - Wavelet-based multiscale proper generalized decomposition JO - Comptes Rendus. Mécanique PY - 2018 SP - 485 EP - 500 VL - 346 IS - 7 PB - Elsevier DO - 10.1016/j.crme.2018.04.013 LA - en ID - CRMECA_2018__346_7_485_0 ER -
%0 Journal Article %A Angel Leon %A Anais Barasinski %A Emmanuelle Abisset-Chavanne %A Elias Cueto %A Francisco Chinesta %T Wavelet-based multiscale proper generalized decomposition %J Comptes Rendus. Mécanique %D 2018 %P 485-500 %V 346 %N 7 %I Elsevier %R 10.1016/j.crme.2018.04.013 %G en %F CRMECA_2018__346_7_485_0
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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