Optimum shape design using automatic differentiation in reverse mode

  • M. Hafez
  • B. Mohammadi
  • O. Pironneau
Algorithms Numerical Techniques
Part of the Lecture Notes in Physics book series (LNP, volume 490)


This paper is devoted to show how to use automatic differentiation in reverse mode as a powerful tool in optimization procedures. It is also shown that for aerodynamic applications the gradients have to be as accurate as possible. In particular, the effect of having the exact gradient of the first or second order spatial discretization schemes is presented. We show that the loss of precision in the gradient affects not only the convergence, but also the final shape. Both two and three dimensional configurations of transonic and supersonic flows have been investigated. These cases involve up to several thousand of control parameters.


Cost Function Control Point Drag Reduction Supersonic Flow Conjugate Gradient Method 
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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • M. Hafez
  • B. Mohammadi
  • O. Pironneau

There are no affiliations available

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