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\title{ON AUTOMATIC DERIVATIVES IN SENSITIVITY ANALYSIS FOR SHAPE OPTIMIZATION PROBLEMS}
\author{MATTI MEIKÄLÄINEN}
\address{Department of Mathematical Information Technology\\
University of Jyv\"askyl\"a\\
P. O. Box 35\\
FIN-40351 Jyv\"askyl\"a, FINLAND\\
e-mail: matti.meikalainen@yliopisto.fi
}

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\section*{ABSTRACT}


This is a LaTeX template only, not scientific paper.
A hybrid approach for shape design sensitivity analysis for a class of
shape optimization is presented. Hand-coded derivatives and automatic
derivatives are combined in such a way that the adjoint equation
technique can be utilized.
This approach yields significant reduction in the memory and time
required to compute derivatives if compared to the approach where 
automatic differentiation is applied to the whole code.
Numerical example is given.

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     Shape optimization for laminar and turbulent flows with
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     Proceedings of the Tenth International Conference on Finite
     Elements in Fluids, M. Hafez and J. C. Heinrich (eds.),
     The University of Arizona, 536--541, 1998.

\bibitem{Moh-Mal-Ros-96}
	B.~Mohammadi, J.-M.~Mal\'e, and N.~Rostaing-Schmidt,
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	Computational Differentiation: Techniques, Applications, and Tools,
	M.~Berz, C.~Bischof, G.~Corlis, and A.~Griewank (eds.),
	SIAM, 1996.


\bibitem{Cha-Ghe-00}
    I.~Charpentier and M.~Ghemires,
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\bibitem{Fau-Dut-Fid-00}
	C.~Faure, P.~Dutto, and S.~Fidanova,
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\bibitem{Gri-89}
 A. Griewank, On Automatic Differentiation,
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