@article {Mohammadi:1996:ADI,
title = {Automatic Differentiation in Direct and Reverse Modes: Application to Optimum Shapes Design in Fluid Mechanics},
journal = {Computational Differentiation: Techniques, Applications, and Tools},
year = {1996},
pages = {309{\textendash}318},
publisher = {SIAM},
address = {Philadelphia, PA},
abstract = {We first give a description of the Odyss{\'e}e system. Odyss{\'e}e takes as input a Fortran program and a set of variables and returns a new Fortran program computing the derivatives of the original function with respect to the given variables. Direct differentiation, producing a Jacobian matrix or a gradient vector, and reverse mode, computing the linear cotangent map, are implemented in Odyss{\'e}e. The available strategies of differentiation are presented: they lead to different computation speeds and memory requirements. We consider problems belonging to optimal shape design in aeronautics. Some implicit functional must be minimized over a set of possible shapes, under the constraint that the stationary Euler equations of the surrounding flow are verified. We describe the physical problems and the numerical methods used for solving them. We discuss the advantages and drawbacks of two different approaches in the use of Odyss{\'e}e for solving the optimization problem. These approaches are analyzed on several tes},
keywords = {AD, aerodynamics, CFD, optimization},
author = {Bijan Mohammadi and Jean-Michel Mal{\'e} and Nicole Rostaing-Schmidt},
editor = {Martin Berz and Christian H. Bischof and George F. Corliss and Andreas Griewank}
}