Skip to main content

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. Di Cesare and O. Pironneau(2000). Shock sensitivity analysis. Computational Fluid Dynamics Journal, vol 9 no 2.

    Google Scholar 

  2. G. Lemarchand, O. Pironneau, E. Polak: Incomplete gradients. Proc Domain Decomposition Method Conf, Lyon 2000. M Garbey ed. (to appear)

    Google Scholar 

  3. G. Lemarchand, O. Pironneau, E. Polak: Incomplete gradients. Proc Domain Decomposition Method Conf, Lyon 2000. M Garbey ed. (to appear)

    Google Scholar 

  4. B. Mohammadi, O. Pironneau: Applied Optimal Shape Design Oxford University Press, 2001.

    Google Scholar 

  5. O. Pironneau. (1984). Optimal shape design for elliptic systems, Springer-Verlag.

    Book  MATH  Google Scholar 

  6. J. Sokolowski and J.P. Zolezio. (1991), Introduction to shape optimization Springer Series in Computational Mathematics.

    Google Scholar 

  7. L. Tartar. (1974). Control problems in the coefficients of PDE, Lecture notes in Economics and Math Systems. A. Bensoussan, Springer Verlag.

    Google Scholar 

  8. J. Hadamard: Leçons sur le calcul des variations. Gauthier-Villars, Paris, (1910).

    MATH  Google Scholar 

  9. H. Attouch, M. Cabot, M. Masmoudi, B. Mohammadi, and P. Redont. Coupling dynamic approaches for global minimization, Journal of Convex Analysis, 25,(2000).

    Google Scholar 

  10. 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)

    Google Scholar 

  11. 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)

    Google Scholar 

  12. A. Grundman, Thesis, University Paul Sabatier, Toulouse, (1998).

    Google Scholar 

  13. Todd L. Veldhuizen, Expression templates, C++ Report vol 7, no 5, pp 26–31, june (1995).

    Google Scholar 

  14. 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.

    Google Scholar 

  15. P.L. George, Automatic mesh generation. Applications to finite element method, Wiley, (1991).

    Google Scholar 

  16. F. Hecht and B. Mohammadi. Mesh adaptation by metric control for multi-scale phenomena and turbulence, American Institute of Aeronautics and Astronautics, 970859,(1997).

    Google Scholar 

  17. M. Farin, Algorithms for C.A.D. Wileyv, 1987.

    Google Scholar 

  18. J. Haslinger, R. Makinen, Introduction to Shape Optimization, SIAM, (2002).

    Google Scholar 

  19. J. Periaux: Optimization with Genetic Algorithm. These proceedings.

    Google Scholar 

  20. M. Schoenauer and Z. Michalewicz. Evolutionary computation: An introduction. Control and Cybernetics, 26(3):307–338, (1997).

    MathSciNet  MATH  Google Scholar 

  21. 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).

    MathSciNet  MATH  Google Scholar 

  22. 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.

    Google Scholar 

  23. 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.

    Google Scholar 

  24. 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.

    Article  MATH  Google Scholar 

  25. 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.

    Google Scholar 

  26. Pironneau O. and Polak E.: Consistent Approximations and Approximate Functions and Gradients In Optimal Control (submitted to SIAM).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-44873-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07294-9

  • Online ISBN: 978-3-540-44873-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics