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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 The Author(s)
About this chapter
Cite this chapter
Chinesta, F., Keunings, R., Leygue, A. (2014). Parametric Models. In: The Proper Generalized Decomposition for Advanced Numerical Simulations. SpringerBriefs in Applied Sciences and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-02865-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-02865-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02864-4
Online ISBN: 978-3-319-02865-1
eBook Packages: EngineeringEngineering (R0)