Parametric Models

  • Francisco Chinesta
  • Roland Keunings
  • Adrien Leygue
Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

Since separated representations allow one to circumvent the curse of dimensionality, one can consider model parameters, boundary conditions, initial conditions or geometrical parameters defining the computational domain, as extra-coordinates of the problem. Thus, standard models become multi-dimensional, but by solving them only once and offline using the PGD, the solution of the model is available for any choice of the parameters considered as extra-coordinates. This parametric solution can then be used online for different purposes, such as real time simulation, efficient optimization or inverse analysis, or simulation-based control. In this chapter, we illustrate the procedures for considering (a) model parameters, (b) constant and non-constant Dirichlet and Neumann boundary conditions, (c) initial conditions and (d) geometrical parameters, as extra-coordinates of a resulting multi-dimensional model.

Keywords

Geometrical parameters Material parameters Parametric boundary conditions Parametric model Parametric solution Proper Generalized Decomposition 

References

  1. 1.
    D. Gonzalez, A. Ammar, F. Chinesta, E. Cueto, Recent advances in the use of separated representations. Int. J. Numer. Meth. Eng. 81(5), 637–659 (2010)Google Scholar
  2. 2.
    A. Ammar, F. Chinesta, E. Cueto, M. Doblare, Proper generalized decomposition of time-multiscale models. Int. J. Numer. Meth. Eng. 90(5), 569–596 (2012)Google Scholar
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    D. Gonzalez, F. Masson, F. Poulhaon, A. Leygue, E. Cueto, F. Chinesta, Proper generalized decomposition based dynamic data-driven inverse identification. Math. Comput. Simul. 82(9), 1677–1695 (2012)Google Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Francisco Chinesta
    • 1
  • Roland Keunings
    • 2
  • Adrien Leygue
    • 1
  1. 1.GeM UMR CNRSEcole Centrale de NantesNantes Cedex 3France
  2. 2.Applied MathematicsUniversité catholique de LouvainLouvain-la-NeuveBelgium

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