Comptes Rendus
no. 7
Model reduction, data-based and advanced discretization in computational mechanics
Algebraic PGD for tensor separation and compression: An algorithmic approach
Pedro Díez1  ; Sergio Zlotnik1 ; Alberto García-González1 ; Antonio Huerta1
1 Laboratori de Càlcul Numèric, E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya – (UPC BarcelonaTech), Jordi Girona 1, 08034 Barcelona, Spain
Comptes Rendus. Mécanique, Volume 346 (2018) no. 7, pp. 501-514.

Proper Generalized Decomposition (PGD) is devised as a computational method to solve high-dimensional boundary value problems (where many dimensions are associated with the space of parameters defining the problem). The PGD philosophy consists in providing a separated representation of the multidimensional solution using a greedy approach combined with an alternated directions scheme to obtain the successive rank-one terms. This paper presents an algorithmic approach to high-dimensional tensor separation based on solving the Least Squares approximation in a separable format of multidimensional tensor using PGD. This strategy is usually embedded in a standard PGD code in order to compress the solution (reduce the number of terms and optimize the available storage capacity), but it stands also as an alternative and highly competitive method for tensor separation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2018.04.011
Mots clés : Tensor separation, Algebraic PGD, Least-squares approximation
Pedro Díez 1 ; Sergio Zlotnik 1 ; Alberto García-González 1 ; Antonio Huerta 1

1 Laboratori de Càlcul Numèric, E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya – (UPC BarcelonaTech), Jordi Girona 1, 08034 Barcelona, Spain 
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     title = {Algebraic {PGD} for tensor separation and compression: {An} algorithmic approach},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {501--514},
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Pedro Díez; Sergio Zlotnik; Alberto García-González; Antonio Huerta. Algebraic PGD for tensor separation and compression: An algorithmic approach. Comptes Rendus. Mécanique, Volume 346 (2018) no. 7, pp. 501-514. doi : 10.1016/j.crme.2018.04.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.04.011/

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