Reduced basis method applied to large non-linear multi-physics problems. Application to high field magnets design.

Abstract : Perfectly characterized since more than 100 years, the magnetic field is present throughout our environment. Besides the numerous possibilities it opens, it constitutes a powerfull tool for researchers especially to probe and determine the properties of the matter. This kind of applications requires nevertheless magnetic fields of high intensity, namely higher than the one achievable by superconducting magnets. The "Laboratoire National des Champs Magnétiques Intenses" (LNCMI) develops water cooled resistive magnets providing such magnetic field to scientists. The design of these magnets represents a challenge in terms of design and materials. The numerical simulation proves essential to achieve such an optimization process. This thesis fits into a research collaboration between the Institut de Recherche Mathématique Avancée (IRMA) and the LNCMI whose goal is the development of a software toolchain for high field magnets modeling. Its primary objective resides in the development of a range of non-linear coupled models taking into account the whole involved physics, except the hydraulic related with the magnet cooling. Based on the finite element method, the resulting multi-physics model is implemented through the Feel++ library. The core ingredients necessary to implement this model are detailled together with its verification and its validation from experimental results when available. Designed for many query context, the reduced basis method applied to the multi-physics model aims to circumvent the complexity of the considered problem. The efficiency it offers especially allows to move towards parametric studies and sensitivity analysis in various concrete applications. Nevertheless, the necessary precomputations hide an important computational cost due to the non-linearity and the non-affine parametrization of the model. In order to reduce the latter, the Simultaneous Empirical interpolation and Reduced basis method is introduced through this thesis.
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Submitted on : Tuesday, October 4, 2016 - 6:08:05 PM
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Cécile Daversin - Catty. Reduced basis method applied to large non-linear multi-physics problems. Application to high field magnets design.. Analysis of PDEs [math.AP]. IRMA (UMR 7501), 2016. English. ⟨tel-01361722v1⟩

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