Wavelet-based multiscale proper generalized decomposition - 18/05/18

Doi : 10.1016/j.crme.2018.04.013

Angel Leon ^a , Anais Barasinski ^a , Emmanuelle Abisset-Chavanne ^b , Elias Cueto ^c , Francisco Chinesta ^d,^{^⁎}
^a GeM Institute, École centrale de Nantes, 1, rue de la Noë, BP 92101, 44321 Nantes cedex 3, France
^b High Performance Computing Institute & ESI GROUP Chair, École centrale de Nantes, 1, rue de la Noë, BP 92101, 44321 Nantes cedex 3, France
^c I3A, University of Zaragoza, Maria de Luna s/n, 50018 Zaragoza, Spain
^d PIMM Laboratory & ESI GROUP Chair, ENSAM ParisTech, 151, boulevard de l'Hôpital, 75013 Paris, France

^⁎Corresponding author.

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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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Keywords : Wavelets, Proper Generalized Decomposition, Multi-resolution, Multi-scale PGD