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Un framework de calcul pour la méthode des bases réduites : applications à des problèmes non-linéaires multi-physiques

Stéphane Veys 1 
1 EDP - Equations aux Dérivées Partielles
LJK - Laboratoire Jean Kuntzmann
Abstract : Today, in many fields of applications, more and more engineering problems require to have an accurate and efficient evaluation of quantities of interest. Often, these quantities depend on a partial differential equation (PDE) parameterized solution -- physical or geometrical -- are the model inputs and the quantities of interest -- average values -- are the outputs. The order reduction techniques, including reduced basis method which is the method used throughout this work, can meet these demands. In this thesis, we focus on the establishment of a framework in C ++ supporting parallel computing, which applies the reduced basis method to nonlinear multiphysics problems such as problems with natural convection (fluid-thermal coupling) or the high field resistive magnet modeling (we limit ourselves to thermo-electric coupling) leading to a study on the uncertainty quantification. The reduced basis method naturally relies on an approximation obtained using the finite element discretization of the problem being treated. For this, we use the Feel ++ computation library specialized in PDE resolution. We are also interested by multiscale problems. The particularity of these problems is to manipulate a set of phenomena involving different scales, as this is the case for example when we consider a flow in porous media. The multiscale finite element method allows having a "global" behavior, linked with large scales, of the problem solution without solving it on small scales. We propose a new construction of multiscale finite element basis functions based on the reduced basis method.
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Submitted on : Saturday, November 1, 2014 - 6:30:48 PM
Last modification on : Tuesday, October 19, 2021 - 11:13:15 PM
Long-term archiving on: : Monday, February 2, 2015 - 5:01:26 PM


  • HAL Id : tel-01079415, version 1


Stéphane Veys. Un framework de calcul pour la méthode des bases réduites : applications à des problèmes non-linéaires multi-physiques. Modélisation et simulation. Université Joseph Fourier (Grenoble I), 2014. Français. ⟨NNT : ⟩. ⟨tel-01079415v1⟩



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