Réduction a priori de modèles thermomécaniques

David Ryckelynck

doi:10.1016/S1631-0721(02)01487-0

Réduction a priori de modèles thermomécaniques

David Ryckelynck ¹

¹ Laboratoire de mécanique des systèmes et des procédés, UMR CNRS-ENSAM-ESEM, École nationale supérieure d'Arts et Métiers, 151, boulevard de l'hôpital, 75013 Paris, France

Comptes Rendus. Mécanique, Volume 330 (2002) no. 7, pp. 499-505.

Résumé
Abstract

La méthode de réduction proposée nécessite aucun calcul préalable de l'état de la structure. Le résidu, défini sur tout l'intervalle de temps, des équations obtenues par la méthode des éléments finis et le développement de Karhunen–Loève permettent de définir un faible nombre de fonctions de base pour la représentation spatiale des champs recherchés. Un algorithme non-incrémental, issu de la méthode LATIN, permet de déterminer ces fonctions de base. Le caractère non-incrémental de l'approche garantit la validité du modèle de taille réduite sur un intervalle de temps recouvrant de fortes évolutions de l'état de la structure.

A model reduction method is proposed for finite element models. A previous computation of the state of the structure is not necessary. Residuals defined over the entire time interval and the Karhunen–Loève method provide basis functions. A non-incremental algorithm, from the LATIN method, is used to compute this basis functions. Because of the non-incremental feature, the reduced order model is representative for a large evolution of the state of the structure.

Reçu le : 2002-02-18
Révisé le : 2002-05-22
Publié le : 2002-01-01

DOI : 10.1016/S1631-0721(02)01487-0

Mots-clés : solides et structures, réduction de modèle, sous-espace de Krylov, développement de Karhunen–Loève, approche non-incrémentale, contact
Keywords: solids and structures, model reduction, Karhunen–Loève expansion, Krylov subspace, non-incremental approach, contact

Affiliations des auteurs :

David Ryckelynck ¹

¹ Laboratoire de mécanique des systèmes et des procédés, UMR CNRS-ENSAM-ESEM, École nationale supérieure d'Arts et Métiers, 151, boulevard de l'hôpital, 75013 Paris, France

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David Ryckelynck. Réduction a priori de modèles thermomécaniques. Comptes Rendus. Mécanique, Volume 330 (2002) no. 7, pp. 499-505. doi : 10.1016/S1631-0721(02)01487-0. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01487-0/

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Antoine Dumon; Cyrille Allery; Amine Ammar Proper Generalized Decomposition method for incompressible flows in stream-vorticity formulation, European Journal of Computational Mechanics, Volume 19 (2010) no. 5-7, p. 591 | DOI:10.3166/ejcm.19.591-617
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D. Ryckelynck A priori hyperreduction method: an adaptive approach, Journal of Computational Physics, Volume 202 (2005) no. 1, pp. 346-366 | DOI:10.1016/j.jcp.2004.07.015 | Zbl:1288.65178

Cité par 15 documents. Sources : Crossref, zbMATH

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