Une approche par modèles réduits pour la résolution de problèmes paramétrés multiphysiques fortement couplés

During design, optimization or predictive maintenance stages, engineers need to test various configurations of loading, geometry or material properties in order to build metamodels, perform sensitivity analyses or adjust uncertain parameters. Repeated calls to numerical models are then required to solve numerous related physical problems. However, such an approach can lead to prohibitive computational costs, especially in a multiphysics framework, which is a major focus of today's studies in cutting-edge industries. Indeed, each simulation involves millions of degrees of freedom, and must encompass several physics and their mutual interactions. In this context, this thesis proposes a computational strategy for efficiently solving many similar multiphysics problems. The developed approach is based on the combination of the LATIN-PGD solver and an initialization procedure that takes advantage of previously performed calculations to tackle a new set of parameters. More specifically, a reduced-order basis is built independently for each physics; each basis is then reused and enriched throughout the calculations when deemed necessary. The performances of the method are illustrated on a test case of representative size involving a strong thermo-mechanical coupling. A complete parametric study, involving around a hundred resolutions, is accelerated by a factor of 5 compared with a naive application of the LATIN-PGD method, and by a factor of 45 in comparison with a conventional monolithic approach.