Summary
In this paper we apply to a few new problems some of the techniques we have developed over the years for optimal shape design. These include optimality conditions, automatic differentiation and the appropriate descent methods.
Dedicated to J.L. Lions who passed away in May 2001. His encouragements and beliefs in scientific computing and optimization, his leadership as a scientific consultant at DassaultAviation played a great role in the career of both of us.
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References
N. Di Cesare and O. Pironneau(2000). Shock sensitivity analysis. Computational Fluid Dynamics Journal, vol 9 no 2.
G. Lemarchand, O. Pironneau, E. Polak: Incomplete gradients. Proc Domain Decomposition Method Conf, Lyon 2000. M Garbey ed. (to appear)
G. Lemarchand, O. Pironneau, E. Polak: Incomplete gradients. Proc Domain Decomposition Method Conf, Lyon 2000. M Garbey ed. (to appear)
B. Mohammadi, O. Pironneau: Applied Optimal Shape Design Oxford University Press, 2001.
O. Pironneau. (1984). Optimal shape design for elliptic systems, Springer-Verlag.
J. Sokolowski and J.P. Zolezio. (1991), Introduction to shape optimization Springer Series in Computational Mathematics.
L. Tartar. (1974). Control problems in the coefficients of PDE, Lecture notes in Economics and Math Systems. A. Bensoussan, Springer Verlag.
J. Hadamard: Leçons sur le calcul des variations. Gauthier-Villars, Paris, (1910).
H. Attouch, M. Cabot, M. Masmoudi, B. Mohammadi, and P. Redont. Coupling dynamic approaches for global minimization, Journal of Convex Analysis, 25,(2000).
C. Bischof and L. Roh and A.J. Mauer-Oats, ADIC: an extensible automatic differentiation tool for ANSI-C, Software Practice and Experience,27,no 12,pp 1427–1456,(1997)
C. Bendtsen and O. Stauning, FADBAD, a flexible C++ package for automatic differentiation using the forward and backward methods, Technical Report IMM-REP-199617,(1996)
A. Grundman, Thesis, University Paul Sabatier, Toulouse, (1998).
Todd L. Veldhuizen, Expression templates, C++ Report vol 7, no 5, pp 26–31, june (1995).
P. Aubert, N. dicesare and O. Pironneau, Automatic Differentiation in C++ using Expression Templates and Application to a Flow Control Problem. Accepted in Computer Visualization and Software, 2000.
P.L. George, Automatic mesh generation. Applications to finite element method, Wiley, (1991).
F. Hecht and B. Mohammadi. Mesh adaptation by metric control for multi-scale phenomena and turbulence, American Institute of Aeronautics and Astronautics, 970859,(1997).
M. Farin, Algorithms for C.A.D. Wileyv, 1987.
J. Haslinger, R. Makinen, Introduction to Shape Optimization, SIAM, (2002).
J. Periaux: Optimization with Genetic Algorithm. These proceedings.
M. Schoenauer and Z. Michalewicz. Evolutionary computation: An introduction. Control and Cybernetics, 26(3):307–338, (1997).
Allaire G., Kohn R.V., Optimal design for minimum weight and compliance in plane stress using extremal microstructures, Europ. J. Mech. A/Solids 12, 6, pp.839–878 (1993).
C. Bischof, A. Carle, G. Corliss, A. Griewank, and P. Hovland, ADIFOR: Generating derivative codes from fortran programs, Scientific Programming, 1(1):11–29, 1992.
Andreas Griewank, David Juedes, and Jean Utke. Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/ C++, j-TOMS, 22(2):131 167, June 1996.
Andreas Griewank, David Juedes, and Jean Utke. Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/ C++, j-TOMS, 22(2):131–167, June 1996.
Bernardi D., F. Hecht, K. Otsuka, O. Pironneau: freefem+, a finite element software to handle several meshes.Dowloadable from ftp://ftp.ann.jussieu.fr/pub/soft/pironneau/, 1999.
Pironneau O. and Polak E.: Consistent Approximations and Approximate Functions and Gradients In Optimal Control (submitted to SIAM).
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Pironneau, O., Mohammadi, B. (2003). Techniques for Optimal Shape Design. In: Barton, N.G., Periaux, J. (eds) Coupling of Fluids, Structures and Waves in Aeronautics. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44873-0_16
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DOI: https://doi.org/10.1007/978-3-540-44873-0_16
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