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Recent Advances and New Challenges in the Use of the Proper Generalized Decomposition for Solving Multidimensional Models

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Abstract

This paper revisits a powerful discretization technique, the Proper Generalized Decomposition—PGD, illustrating its ability for solving highly multidimensional models. This technique operates by constructing a separated representation of the solution, such that the solution complexity scales linearly with the dimension of the space in which the model is defined, instead the exponentially-growing complexity characteristic of mesh based discretization strategies. The PGD makes possible the efficient solution of models defined in multidimensional spaces, as the ones encountered in quantum chemistry, kinetic theory description of complex fluids, genetics (chemical master equation), financial mathematics, … but also those, classically defined in the standard space and time, to which we can add new extra-coordinates (parametric models, …) opening numerous possibilities (optimization, inverse identification, real time simulations, …).

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Authors and Affiliations

  1. EADS Corporate Fundation International Chair, GEM, UMR CNRS–Centrale Nantes, 1 rue de la Noe, BP 92101, 44321, Nantes Cedex 3, France

    Francisco Chinesta

  2. Arts et Métiers ParisTech, 2 Boulevard du Ronceray, BP 93525, 49035, Angers Cedex 01, France

    Amine Ammar

  3. Group of Structural Mechanics and Materials Modelling, Aragón Institute of Engineering Research (I3A), Universidad de Zaragoza, Maria de Luna, 3, 50018, Zaragoza, Spain

    Elías Cueto

Authors
  1. Francisco Chinesta
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  2. Amine Ammar
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  3. Elías Cueto
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Correspondence to Francisco Chinesta.

Additional information

Research partially supported by the Spanish Ministry of Science ad Innovation through grant CICYT-DPI2008-00918.

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Chinesta, F., Ammar, A. & Cueto, E. Recent Advances and New Challenges in the Use of the Proper Generalized Decomposition for Solving Multidimensional Models. Arch Computat Methods Eng 17, 327–350 (2010). https://doi.org/10.1007/s11831-010-9049-y

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  • DOI: https://doi.org/10.1007/s11831-010-9049-y

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