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Optimization loops for shape and error control: extended lecture notes

Abstract : The power and versatility of the so-called adjoint methods used in optimization problems is addressed by presenting a combined methodology: shape and error control. In a first part we describe novel technologies for solving shape design problems: constrained optimum formulation with adjoint, one-shot optimization algorithms and multi-level optimization preconditioning. The application to a shape design problem related to sonic boom minimization is reported. In a second part, after some remarks on mesh adaptation, we examine the problem of formulating mesh adaptation in terms of an optimization problem, presenting some applications to interpolation and to Partial Differential Equations. The implications of the proposed method become clear: by combining together both ideas cost effective methods can be developed where the optimization loops involve both shape optimization, to improve an aerodynamic design, and mesh adaptivity, to cope with the difficulties of the CFD problem involved. Ce document présente la version détaillée des notes de cours au ``PROMUVAL Short Course on Multidisciplinary Modelling Simulation and Validation in Aeronautics'', qui s'est tenu à Barcelone (E), les 28-29 juin 2004.
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https://hal.inria.fr/inria-00070593
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Submitted on : Friday, May 19, 2006 - 8:57:52 PM
Last modification on : Monday, July 23, 2018 - 2:20:01 PM
Long-term archiving on: : Sunday, April 4, 2010 - 9:32:17 PM

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Alain Dervieux, F. Courty, Tristan Roy, M. Vázquez, B. Koobus. Optimization loops for shape and error control: extended lecture notes. [Research Report] RR-5413, INRIA. 2006, pp.41. ⟨inria-00070593⟩

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