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We study the application of a multi-level preconditioner to a practical optimal shape design problem. The preconditioner is based on the Bramble-Pasciak-Xu series. We extend it to the unstructured parametrization of 3D shapes by using the volume-agglomeration heuristics. The choice of the smoothing parameter is analysed from functional arguments. Application to the shape design for optimising aerodynamic and sonic boom performances of a wing is demonstrated.

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Both continuous and discrete sensititivites and gradient evaluations carry important information in the building of an optimal shape loop. This is particularly true for the smoothness of objective functionals and the functions representing their gradients. The main application addressed here is the choice of a preconditioner for the optimisation loop. Résumé. Gradient continu, gradient discret, tous deux nous apportent des informations importantes pour les boucles de conception optimale de forme, notamment en ce qui concerne la régularité des fonctionnelles et des fonctions constituées par leur gradients. La principale application présentée est le choix d'un préconditionneur pour la boucle d'optimisation.