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Optimisation Différentiable en Mécanique des Fluides Numérique

Francois Courty 1 
1 TROPICS - Program transformations for scientific computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Our contribution concerns the following three complementary domains: Automatic Differentiation, optimal shape design for large systems, mesh adaption. In the chapter 1 of the part 1, we expose a method to compute gradients using Automatic Differentiation for a classical optimal shape design problem. We explain how to deduce an exact gradient based on an adjoint state without storing explicitly the Jacobian matrix. In the chapter 2 of the part 2, we propose a SQP-like method to solve a class of optimization problems with equality constraints. The new algorithm enables to solve simultaneously the optimality system. In the chapter 3 of the part 2, we study a new preconditioning strategy for optimal shape design. We build an additive multilevel preconditioning starting from the classical Bramble-Pasciak-Xu principle and from the agglomeration principle. In the chapter 1 of the part 3, we study the problem of the best adapted mesh for a pure interpolation problem. The optimality system solution gives a completely explicite expression of the optimal metric as a function of the function to adapt. In the chapter 2 of the part 3, we extend the method of the previous chapter to the problem of mesh adaption for P.D.E. We obtain an optimal control formulation with an adjoint state.
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Submitted on : Tuesday, January 27, 2004 - 5:57:43 PM
Last modification on : Friday, February 4, 2022 - 3:08:51 AM
Long-term archiving on: : Friday, April 2, 2010 - 8:06:15 PM


  • HAL Id : tel-00004344, version 1



Francois Courty. Optimisation Différentiable en Mécanique des Fluides Numérique. Mathématiques [math]. Université Paris Sud - Paris XI, 2003. Français. ⟨tel-00004344⟩



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