BibTeX
@INCOLLECTION{
Mohammadi1996ADi,
author = "Bijan Mohammadi and JeanMichel Mal{\'e} and Nicole RostaingSchmidt",
editor = "Martin Berz and Christian H. Bischof and George F. Corliss and Andreas Griewank",
title = "Automatic Differentiation in Direct and Reverse Modes: {A}pplication to Optimum Shapes
Design in Fluid Mechanics",
booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
pages = "309318",
publisher = "SIAM",
address = "Philadelphia, PA",
key = "Mohammadi1996ADi",
crossref = "Berz1996CDT",
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 = "Optimum shape design, computational fluid mechanics, aeronautics,
Odyss{\'e}e.",
referred = "[Bischof1996HAt], [Hascoet2002AIC].",
year = "1996"
}
