Abstract
We begin by recalling the classical approach to solve shape design problems by gradient methods. Then we proceed to explain how automatic differentiation can simplify the analysis and illustrate this approach to a shape design problem where the shock is required to be at a certain place. The object of this chapter is to show that automatic differentiation seems to work even though the gradients and the calculus of variation have to be extended by Distribution theory.
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References
A. Griewank: Evaluating Derivatives, Principles and Techniques of Algorithmic Differentiation. Vol 19, Frontiers in Applied Mathematics. SIAM, Philadelphia. (2000).
B. Mohammadi and O. Pironneau: Applied Numerical Optimal Shape Design. Oxford U. Press. (2001).
A. Caughey and M. Hafez (ed.): Pros and Cons of Airfoil Optimization, Frontier of Computational Fluid Dynamics, World Scientific, Singapore. (1998).
C. Bardos and O. Pironneau : Derivatives and Control in the Presence of Shocks. Computational Fluid Dynamics Journal, vol 12, no.1 (April 2003).
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© 2009 Springer-Verlag New York
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Pironneau, O. (2009). Shock Optimization for Airfoil Design Problems. In: Variational Analysis and Aerospace Engineering. Springer Optimization and Its Applications, vol 33. Springer, New York, NY. https://doi.org/10.1007/978-0-387-95857-6_20
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DOI: https://doi.org/10.1007/978-0-387-95857-6_20
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Publisher Name: Springer, New York, NY
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Online ISBN: 978-0-387-95857-6
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