Free Access
Issue
ESAIM: COCV
Volume 14, Number 3, July-September 2008
Page(s) 427 - 455
DOI https://doi.org/10.1051/cocv:2007059
Published online 21 November 2007
  1. G. Allaire, F. de Gournay, F. Jouve and A.-M. Toader, Structural optimization using topological and shape sensitivity via a level set method. Control Cybern. 34 (2005) 59–80. [Google Scholar]
  2. H. Ammari and H. Kang, Reconstruction of small inhomogeneities from boundary measurements, Lecture Notes in Mathematics 1846. Springer-Verlag, Berlin (2004). [Google Scholar]
  3. H. Ammari and H. Kang, Reconstruction of elastic inclusions of small volume via dynamic measurements. Appl. Math. Optim. 54 (2006) 223–235. [CrossRef] [MathSciNet] [Google Scholar]
  4. H. Ammari and H. Kang, Generalized polarization tensors, inverse conductivity problems, and dilute composite materials: a review, in Inverse problems, multi-scale analysis and effective medium theory, Contemp. Math. 408, Amer. Math. Soc., Providence, RI (2006) 1–67. [Google Scholar]
  5. S. Amstutz, Sensitivity analysis with respect to a local perturbation of the material property. Asymptotic Anal. 49 (2006) 87–108. [Google Scholar]
  6. S. Amstutz and H. Andrä, A new algorithm for topology optimization using a level-set method. J. Comput. Phys. 216 (2006) 573–588. [CrossRef] [MathSciNet] [Google Scholar]
  7. S. Amstutz and N. Dominguez, Topological sensitivity analysis in the context of ultrasonic nondestructive testing. RICAM report 2005-21 (2005). [Google Scholar]
  8. S. Amstutz, I. Horchani and M. Masmoudi, Crack detection by the topological gradient method. Control Cybern. 34 (2005) 81–101. [Google Scholar]
  9. M. Bonnet, Topological sensitivity for 3d elastodynamic and acoustic inverse scattering in the time domain. Comput. Meth. Appl. Mech. Engrg. 195 (2006) 5239–5254. [CrossRef] [Google Scholar]
  10. M. Bonnet and B.B. Guzina, Sounding of finite solid bodies by way of topological derivative. Int. J. Numer. Methods Eng. 61 (2004) 2344–2373. [CrossRef] [Google Scholar]
  11. M. Burger, B. Hackl and W. Ring, Incorporating topological derivatives into level set methods. J. Comput. Phys. 194 (2004) 344–362. [CrossRef] [MathSciNet] [Google Scholar]
  12. T. Cazenave and A. Haraux, Introduction aux problèmes d'évolution semi-linéaires, Mathématiques & Applications 1. Ellipses, Paris (1990). [Google Scholar]
  13. R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 6. INSTN: Collection Enseignement, Masson, Paris (1988). [Google Scholar]
  14. H.A. Eschenauer and A. Schumacher, Topology and shape optimization procedures using hole positioning criteria — theory and applications, in Topology optimization in structural mechanics, CISM Courses and Lectures 374, Springer, Vienna (1997) 135–196. [Google Scholar]
  15. H.A. Eschenauer, V.V. Kobolev and A. Schumacher, Bubble method for topology and shape optimization of structures. Struct. Optimization 8 (1994) 42–51. [CrossRef] [Google Scholar]
  16. S. Garreau, P. Guillaume and M. Masmoudi, The topological asymptotic for PDE systems: the elasticity case. SIAM J. Control Optim. 39 (2001) 1756–1778 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  17. P. Guillaume and K. Sid Idris, The topological asymptotic expansion for the Dirichlet problem. SIAM J. Control Optim. 41 (2002) 1042–1072 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  18. B.B. Guzina and M. Bonnet, Topological derivative for the inverse scattering of elastic waves. Quart. J. Mech. Appl. Math. 57 (2004) 161–179. [CrossRef] [MathSciNet] [Google Scholar]
  19. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 2. Travaux et Recherches Mathématiques 18. Dunod, Paris (1968). [Google Scholar]
  20. S.A. Nazarov and J. Sokolowski, The topological derivative of the Dirichlet integral under the formation of a thin bridge. Siberian Math. J. 45 (2004) 341–355. [CrossRef] [MathSciNet] [Google Scholar]
  21. G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics. Annals of Mathematics Studies 27. Princeton University Press, Princeton, N. J. (1951). [Google Scholar]
  22. J. Pommier and B. Samet, The topological asymptotic for the Helmholtz equation with Dirichlet condition on the boundary of an arbitrarily shaped hole. SIAM J. Control Optim. 43 (2004) 899–921 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  23. M. Schiffer and G. Szegö, Virtual mass and polarization. Trans. Amer. Math. Soc. 67 (1949) 130–205. [MathSciNet] [Google Scholar]
  24. A. Schumacher, Topologieoptimierung von bauteilstrukturen unter verwendung von lopschpositionierungskriterien. Ph.D. thesis, Univ. Siegen (1995). [Google Scholar]
  25. J. Sokołowski and A. Żochowski, On the topological derivative in shape optimization. SIAM J. Control Optim. 37 (1999) 1251–1272 (electronic). [CrossRef] [MathSciNet] [Google Scholar]

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