Free Access
Volume 14, Number 1, January-March 2008
Page(s) 160 - 191
Published online 21 September 2007
  1. M. Abdelwahed, M. Amara, F. El Dabaghi and M. Hassine, A numerical modelling of a two phase flow for water eutrophication problems. ECCOMAS 2000, European Congress on Computational Methods in Applied Sciences and Engineering, Barcelone, 11–14 September (2000). [Google Scholar]
  2. G. Allaire and A. Henrot, On some recent advances in shape optimization. C. R. Acad. Sci. Paris, Ser. II B 329 (2001) 383–396. [Google Scholar]
  3. G. Allaire and R. Kohn, Optimal bounds on the effective behavior of a mixture of two well-orded elastic materials. Quart. Appl. Math. 51 (1996) 643–674. [Google Scholar]
  4. G. Allaire, F. Jouve and A.-M. Toader, Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194 (2004) 363–393. [CrossRef] [Google Scholar]
  5. S. Amstutz, M. Masmoudi and B. Samet, The topological asymptotic for the Helmholtz equation. SIAM J. Contr. Optim. 42 (2003) 1523–1544. [Google Scholar]
  6. J.A. Bello, E. Fernández-Cara, J. Lemoine and J. Simon, The differentiability of the drag with respect to the variations of a lipschitz domain in a Navier-Stokes flow. SIAM J. Control Optim. 35 (1997) 626–640. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. Bendsoe, Optimal topology design of continuum structure: an introduction. Technical report, Departement of mathematics, Technical University of Denmark, DK2800 Lyngby, Denmark (1996). [Google Scholar]
  8. M. Bendsoe, N. Olhoff and O. Sigmund, IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials. Springer (2006). [Google Scholar]
  9. F. Brezzi and M. Fortin, Mixed and hybrid finite element method, Springer Series in Computational Mathematics 15. Springer Verlag- New York (1991). [Google Scholar]
  10. G. Buttazzo and G. Dal Maso, Shape optimization for Dirichlet problems: Relaxed formulation and optimality conditions. Appl. Math. Optim. 23 (1991) 17–49. [Google Scholar]
  11. J. Céa, Conception optimale ou identification de forme, calcul rapide de la dérivée directionnelle de la fonction coút. RAIRO Math. Modél. Anal. Numér. 20 (1986) 371–402. [Google Scholar]
  12. J. Céa, A. Gioan and J. Michel, Quelques résultats sur l'identification de domains. Calcolo (1973). [Google Scholar]
  13. J. Céa, S. Garreau, P. Guillaume and M. Masmoudi, The shape and topological optimizations connection. Comput. Methods Appl. Mech. Engrg. 188 (2000) 713–726. [CrossRef] [MathSciNet] [Google Scholar]
  14. M. Chipot and G. Dal Maso, Relaxed shape optimization: the case of nonnegative data for the Dirichlet problems. Adv. Math. Sci. Appl. 1 (1992) 47–81. [MathSciNet] [Google Scholar]
  15. P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland (1978). [Google Scholar]
  16. R. Dautray and J. Lions, Analyse mathémathique et calcul numérique pour les sciences et les techniques. Masson, collection CEA (1987). [Google Scholar]
  17. S. Garreau, P. Guillaume and M. Masmoudi, The topological asymptotic for pde systems: the elasticity case. SIAM J. Control Optim. 39 (2001) 1756–1778. [Google Scholar]
  18. V. Girault and P.A. Raviart, Finite element methods for Navier-Stokes equations, Theory and Algorithms. Springer Verlag (1986). [Google Scholar]
  19. R. Glowinski and O. Pironneau, Toward the computational of minimun drag profile in viscous laminar flow. Appl. Math. Model. 1 (1976) 58–66. [CrossRef] [Google Scholar]
  20. P. Guillaume, Dérivées d'ordre supérieur en conception optimale de forme. Ph.D. thesis, Université Paul Sabatier, Toulouse, France (1994). [Google Scholar]
  21. P. Guillaume and M. Masmoudi, Computation of high order derivatives in optimal shape design. Numer. Math. 67 (1994) 231–250. [CrossRef] [Google Scholar]
  22. P. Guillaume and K. Sid Idris, The topological asymptotic expansion for the Dirichlet Problem. SIAM J. Control. Optim. 41 (2002) 1052–1072. [Google Scholar]
  23. P. Guillaume and K. Sid Idris, Topological sensitivity and shape optimization for the Stokes equations. SIAM J. Control Optim. 43 (2004) 1–31. [CrossRef] [MathSciNet] [Google Scholar]
  24. M.D. Gunzburger and H. Kim, Existence of an optimal solution of a shape control problem for the stationary Navier-Stokes equations. SIAM J. Control Optim. 36 (1998) 895–909. [CrossRef] [MathSciNet] [Google Scholar]
  25. M. Hassine and M. Masmoudi, The topological sensitivity analysis for the Quasi-Stokes problem. ESAIM: COCV 10 (2004) 478–504. [CrossRef] [EDP Sciences] [Google Scholar]
  26. J. Jacobsen, N. Olhoff and E. Ronholt, Generalized shape optimization of three-dimensionnal structures using materials with optimum microstructures. Technical report, Institute of Mechanical Engineering, Aalborg University, DK-9920 Aalborg, Denmark (1996). [Google Scholar]
  27. J.L. Lions and E. Magenes, Problèmes aux limites non homogenes et applications. Dunod (1968). [Google Scholar]
  28. M. Masmoudi, The topological asymptotic, in Computational Methods for Control Applications, H. Kawarada and J. Periaux Eds., International Séries Gakuto (2002). [Google Scholar]
  29. M. Masmoudi, J. Pommier and B. Samet, The topological asymptotic expansion for the Maxwell equations and some applications. Inverse Probl. 21 (2005) 547–564. [Google Scholar]
  30. V. Mazja, S.A. Nazarov and B.A. Plamenevski, Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Vol. I, Birkhäuser (2000). [Google Scholar]
  31. O. Pironneau, On optimum profiles in Stokes flow. J. Fluid Mech. 59 (1973) 117–128. [Google Scholar]
  32. O. Pironneau, Optimal Shape Design for Elliptic Systems. Springer, Berlin (1984). [Google Scholar]
  33. A. Schumacher, Topologieoptimierung von bauteilstrukturen unter verwendung von lopchpositionierungkrieterien. Ph.D. thesis, Universitat-Gesamthochschule-Siegen (1995). [Google Scholar]
  34. M. Shœnauer, L. Kallel and F. Jouve, Mechanical inclusions identification by evolutionary computation. Revue européenne des éléments finis 5 (1996) 619–648. [Google Scholar]
  35. J. Simon, Domain variation for Stokes flow, in Lect. Notes Control Inform. Sci. 159, X. Li and J. Yang Eds., Springer, Berlin (1990) 28–42. [Google Scholar]
  36. J. Simon, Domain variation for drag Stokes flows, in Lect. Notes Control Inform. Sci. 114, A. Bermudez Eds., Springer, Berlin (1987) 277–283. [Google Scholar]
  37. J. Sokolowski and A. Zochowski, On the topological derivative in shape optimization. SIAM J. Control Optim. 37 (1999) 1251–1272 (electronic) [CrossRef] [MathSciNet] [Google Scholar]
  38. J. Sokolowski and A. Zochowski, Modelling of topological derivatives for contact problems. Numer. Math. 102 (2005) 145–179. [CrossRef] [MathSciNet] [Google Scholar]
  39. R. Temam, Navier Stokes equations (1985). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.