Adaptation et réduction de modèle dans les couplages local-global non-intrusifs : application à la conception robuste

This research work focuses on the so-called non-intrusive local-global model coupling procedure which has been proposed and widely analyzed and applied in structural mechanics during the last decade, and which constitutes a flexible and effective engineering simulation tool for the analysis of localized phenomena with low implementation effort. In this context, we propose a specific verification technique, constructed from the Constitutive Relation Error concept, that enables to certify the quality of approximate solutions obtained from such a nonintrusive model coupling. It consists in computable and reliable a posteriori error estimator and indicators in order to quantitatively assess the overall error level and its various sources. It particularly permits the practical control of the error on outputs of interest which are used for design purposes. An adaptive algorithm is then defined in order to effectively and automatically drive the coupling process, and optimally adjust the coupling parameters (location of the coupling interface, local mesh size, number of iterations) so that a given error tolerance is reached with minimal computing resources. The approach is analyzed for various coupling scenarios, including nonlinear local models or local use of PGD reduced order modeling. Its performance is shown on several numerical experiments involving various quantities of interest. It is also applied in the context of tolerance analysis in order to conduct fast and certified computations for optimal or robust design.