Dans la frontière du simulable et au-delà: quand la dimension des modèles devient inimaginable

HAL Id: hal-01495822

https://hal.archives-ouvertes.fr/hal-01495822

Submitted on 26 Mar 2017

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dimension des modèles devient inimaginable

Francisco Chinesta, Amine Ammar

To cite this version:

Francisco Chinesta, Amine Ammar. Dans la frontière du simulable et au-delà: quand la dimension des modèles devient inimaginable. 8e Colloque national en calcul des structures, CSMA, May 2007, Giens, France. �hal-01495822�

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1LMSP UMR 8106 CNRS-ENSAM-ESEM

151 Boulevard de l’Hôpital, F-75013 Paris, France francisco.chinesta@paris.ensam.fr

2Laboratoire de Rhéologie, UMR 5520 CNRS – INPG – UJF 1301 rue de la piscine, BP 53 Domaine universitaire

38041 Grenoble Cedex 9, France Amine.Ammar@ujf-grenoble.fr

RÉSUMÉ. Dans les dernières années nous avons pu assister à une progression sans précédent des performances de la simulation numérique suite à la croissance de la puissance informatique et au développement des méthodes numériques. De nouvelles échelles ont pu être analysées, permettant une modélisation fine et précise de la matière. Dans ce travail nous allons considérer certains modèles définis dans des espaces multidimensionnels dont le traitement numérique était, encore jusqu’à aujourd’hui, considéré comme inimaginable.

ABSTRACT. In the last years, we have assisted to an impressive progression in the numerical modeling capabilities because of the progression in computer science but also in the numerical analysis. Thus, new scales have been explored, allowing modeling of richer and finer physical models. In this work we focus on some models which result defined in multi- dimensional spaces, which have been until now assumed intractable.

MOTS-CLÉS : Simulation numérique, Modèles Multidimensionnels, Réduction de modèles, Séparation de variables.

KEYWORDS: Numerical modeling, Multi-dimensional models, Model reduction, Separated representations.

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