Differentiable and Quasi-Differentiable Methods for Optimal Shape Design in Aerospace

author: Olivier Pironneau, Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie (UPMC)
published: July 20, 2009,   recorded: July 2009,   views: 390


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Optimal shape design can be approached either as an unknown boundary problems as done for most problems of fluid dynamics or as an unknown domain problem as done in structural mechanics for topological optimization. We shall present both methods together with some applications in aerospace. Problems are discretized by the finite element method; differentiable optimization is used when possible and pseudo differentiable methods for topological optimization. Shape optimization is usually computer intensive and parallel computing is a necessity. While evolutionary methods have an edge, gradient methods can be parallelized by domain decomposition just as well. But sensitivity evaluation is too computer intensive and problematic when black-box solvers are used. Data learning and surrogated models can be applied to provide low-fidelity models for the state. These can be used in gradient free, quasi-differentiable or differentiable minimization methods. Then incomplete sensitivity can be used to upgrade data learning at zero cost beyond what available with just the functional. This extra information also gives insights on robustness of the design and allows to discriminate between Pareto points. It also enables the user to have ideas on the impact of uncertainties in independent parameters which are not design parameter. This ensemble leads to a design method, may be less efficient for academic problems, but more robust and reliable in realistic situations with uncertainties on all parameters.

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