A gradient-based method coupled with a multilevel approach is proposed for shape design in aerodynamics. This method extends an existing multilevel gradient-based formulation to another type of control subspaces, i.e. considering another set of subparametrisations and prolongation op- erators. More precisely, Bezier control points associated with the property of degree elevation are involved instead of shape grid-points coordinates and polynomial interpolation. The good behaviour of the new formulation is demonstrated on a classical 2D nozzle inverse problem considering an adjoint formulation as well as an approximate gradient associated to a one-shot method. Resume. Une methode de type gradient associeeune approche multiniveau est proposee dans le cadre de problemes d'optimisation de forme en aerodynamique. Cette methode generalise une formulation deja existante de methode de gradient multiniveau considerant un autre type de sous- espace de controle, c'estdire considerant un autre ensemble de sous-parametrisation et d'operateur de prolongement. Plus precisement, des points de controle de Bezier associesla propriete d'´elevation de degre sont utilises au lieu des coordonnees des points du maillage sur la frontiere et une interpolation polynomiale. Le bon comportement de la nouvelle formulation est illustre pour le cas d'un probleme inverse classique d'une tuyere bidimensionelle considerant aussi bien une methode de l'adjoint que le calcul d'un gradient approche associeune methode de type "one-shot".
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