Proper generalized decomposition of multiscale models

Authors

  • F. Chinesta,

    Corresponding author
    1. EADS Corporate International Chair, GeM—Institut de Recherche en Génie Civil et Mécanique, UMR CNRS-ECN-Université de Nantes, 1 rue de la Noe, BP 92101, F-44321 Nantes Cedex 3, France
    • EADS Corporate International Chair, GeM—Institut de Recherche en Génie Civil et Mécanique, UMR CNRS-ECN-Université de Nantes, 1 rue de la Noe, BP 92101, F-44321 Nantes Cedex 3, France
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  • A. Ammar,

    1. Laboratoire de Rhéologie, UMR CNRS-INPG-UJF, 1301 rue de la piscine, BP 53 Domaine Universitaire, F-38041 Grenoble Cedex 9, France
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  • E. Cueto

    1. Group of Structural Mechanics and Material Modelling, Aragón Institute of Engineering Research, I3A, Universidad de Zaragoza, Edificio Betancourt, María de Luna, 7, E-50012 Zaragoza, Spain
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Abstract

In this paper the coupling of a parabolic model with a system of local kinetic equations is analyzed. A space–time separated representation is proposed for the global model (this is simply the radial approximation proposed by Pierre Ladeveze in the LATIN framework (Non-linear Computational Structural Mechanics. Springer: New York, 1999)). The originality of the present work concerns the treatment of the local problem, that is first globalized (in space and time) and then fully globalized by introducing a new coordinate related to the different species involved in the kinetic model. Thanks to the non-incremental nature of both discrete descriptions (the local and the global one) the coupling is quite simple and no special difficulties are encountered by using heterogeneous time integrations. Copyright © 2009 John Wiley & Sons, Ltd.

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