Free Access
Issue
ESAIM: M2AN
Volume 50, Number 4, July-August 2016
Page(s) 1241 - 1267
DOI https://doi.org/10.1051/m2an/2015075
Published online 14 July 2016
  1. D. Adalsteinsson and J.A. Sethian, A fast level set method for propagating interfaces. J. Comput. Phys. 118 (1995) 269–277. [CrossRef] [MathSciNet] [Google Scholar]
  2. L. Afraites, M. Dambrine and D. Kateb, Shape methods for the transmission problem with a single measurement. Numer. Funct. Anal. Optim. 28 (2007) 519–551. [Google Scholar]
  3. 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]
  4. Z. Belhachmi and H. Meftahi, Shape sensitivity analysis for an interface problem via minimax differentiability. Appl. Math. Comput. 219 (2013) 6828–6842. [CrossRef] [MathSciNet] [Google Scholar]
  5. L. Borcea, Electrical impedance tomography. Inverse Problems 18 (2002) R99–R136. [CrossRef] [Google Scholar]
  6. A.-P. Calderón, On an inverse boundary value problem. In Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980). Soc. Brasil. Mat., Rio de Janeiro (1980) 65–73. [Google Scholar]
  7. A. Canelas, A. Laurain and A.A. Novotny, A new reconstruction method for the inverse potential problem. J. Comput. Phys. 268 (2014) 417–431. [CrossRef] [MathSciNet] [Google Scholar]
  8. A. Canelas, A. Laurain and A.A. Novotny, A new reconstruction method for the inverse source problem from partial boundary measurements. Inverse Problems 31 (2015) 075009. [CrossRef] [MathSciNet] [Google Scholar]
  9. J. Céa, Conception optimale ou identification de formes: calcul rapide de la dérivée directionnelle de la fonction coût. RAIRO M2AN 20 (1986) 371–402. [Google Scholar]
  10. M. Cheney, D. Isaacson and J.C. Newell, Electrical impedance tomography. SIAM Rev. 41 (1999) 85–101 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  11. E.T. Chung, T.F. Chan and X.-C. Tai, Electrical impedance tomography using level set representation and total variational regularization. J. Comput. Phys. 205 (2005) 357–372. [CrossRef] [MathSciNet] [Google Scholar]
  12. M.C. Delfour and J.-P. Zolésio, Shape sensitivity analysis via min max differentiability. SIAM J. Control Optim. 26 (1988) 834–862. [CrossRef] [MathSciNet] [Google Scholar]
  13. M.C. Delfour and J.-P. Zolésio, Shapes and geometries. Metrics, analysis, differential calculus, and optimization. Vol. 22 of Advances in Design and Control, 2nd edn. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2011). [Google Scholar]
  14. J.D. Eshelby, The elastic energy-momentum tensor. Special issue dedicated to A.E. Green. J. Elasticity 5 (1975) 321–335. [CrossRef] [MathSciNet] [Google Scholar]
  15. P. Fulmanski, A. Laurain and J.-F. Scheid, Level set method for shape optimization of Signorini problem. In MMAR Proceedings (2004) 71–75. [Google Scholar]
  16. P. Fulmański, A. Laurain, J.-F. Scheid and J. Sokołowski, A level set method in shape and topology optimization for variational inequalities. Int. J. Appl. Math. Comput. Sci. 17 (2007) 413–430. [MathSciNet] [Google Scholar]
  17. P. Fulmański, A. Laurain, J.-F. Scheid and J. Sokołowski, Level set method with topological derivatives in shape optimization. Int. J. Comput. Math. 85 (2008) 1491–1514. [CrossRef] [MathSciNet] [Google Scholar]
  18. P. Fulmanski, A. Laurain, J.-F. Scheid and J. Sokolowski, Une méthode levelset en optimisation de formes. In CANUM 2006 – Congrès National d’Analyse Numérique. Vol. 22 of ESAIM Proc. Survey EDP Sciences, Les Ulis (2008) 162–168. [Google Scholar]
  19. J. Hadamard, Mémoire sur le probleme d’analyse relatif a l’équilibre des plaques élastiques. In Mémoire des savants étrangers, 33, 1907, Œuvres de Jacques Hadamard. Editions du C.N.R.S., Paris (1968) 515–641. [Google Scholar]
  20. A. Henrot and M. Pierre, Variation et optimisation de formes. Une analyse géométrique. [A geometric analysis]. Vol. 48 of Math. Appl. Springer, Berlin (2005). [Google Scholar]
  21. F. Hettlich, The domain derivative of time-harmonic electromagnetic waves at interfaces. Math. Methods Appl. Sci. 35 (2012) 1681–1689. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Hintermüller and A. Laurain, Electrical impedance tomography: from topology to shape. Control Cybernet. 37 (2008) 913–933. [MathSciNet] [Google Scholar]
  23. M. Hintermüller and A. Laurain, Multiphase image segmentation and modulation recovery based on shape and topological sensitivity. J. Math. Imaging Vision 35 (2009) 1–22. [CrossRef] [MathSciNet] [Google Scholar]
  24. M. Hintermüller and A. Laurain, Optimal shape design subject to elliptic variational inequalities. SIAM J. Control Optim. 49 (2011) 1015–1047. [CrossRef] [MathSciNet] [Google Scholar]
  25. M. Hintermüller, A. Laurain and A.A. Novotny, Second-order topological expansion for electrical impedance tomography. Adv. Comput. Math. (2011) 1–31. [Google Scholar]
  26. M. Hintermüller, A. Laurain and I. Yousept, Shape sensitivities for an inverse problem in magnetic induction tomography based on the eddy current model. Inverse Problems 31 (2015) 065006. [CrossRef] [MathSciNet] [Google Scholar]
  27. R. Hiptmair, A. Paganini and S. Sargheini, Comparison of approximate shape gradients. BIT 55 (2015) 459–485. [CrossRef] [MathSciNet] [Google Scholar]
  28. D. Hömberg and J. Sokołowski, Optimal shape design of inductor coils for surface hardening. SIAM J. Control Optim. 42 (2003) 1087–1117 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  29. R. Kress, Inverse problems and conformal mapping. Complex Var. Elliptic Equ. 57 (2012) 301–316. [CrossRef] [MathSciNet] [Google Scholar]
  30. A. Logg, K.-A. Mardal and G.N. Wells, editors, Automated Solution of Differential Equations by the Finite Element Method. Vol. 84 of Lecture Notes in Computational Science and Engineering. Springer (2012). [Google Scholar]
  31. J.L. Mueller and S. Siltanen, Linear and nonlinear inverse problems with practical applications. Vol. 10 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2012). [Google Scholar]
  32. M. Nagumo, Über die Lage der Integralkurven gewöhnlicher Differentialgleichungen. Proc. Phys. Math. Soc. Japan 24 (1942) 551–559. [MathSciNet] [Google Scholar]
  33. A.A. Novotny and J. Sokołowski, Topological derivatives in shape optimization. Interaction of Mechanics and Mathematics. Springer, Heidelberg (2013). [Google Scholar]
  34. S. Osher and J.A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79 (1988) 12–49. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  35. S. Osher and C.-W. Shu, High-order essentially nonoscillatory schemes for Hamilton–Jacobi equations. SIAM J. Numer. Anal. 28 (1991) 907–922. [CrossRef] [MathSciNet] [Google Scholar]
  36. S. Osher and R. Fedkiw, Level set methods and dynamic implicit surfaces. Vol. 153 of Applied Mathematical Sciences. Springer–Verlag, New York (2003). [Google Scholar]
  37. O. Pantz, Sensibilité de l’équation de la chaleur aux sauts de conductivité. C. R. Math. Acad. Sci. Paris 341 (2005) 333–337. [CrossRef] [MathSciNet] [Google Scholar]
  38. D. Peng, B. Merriman, S. Osher, H. Zhao and M. Kang, A PDE-based fast local level set method. J. Comput. Phys. 155 (1999) 410–438. [CrossRef] [MathSciNet] [Google Scholar]
  39. M. Renardy and R.C. Rogers. An introduction to partial differential equations. Vol. 13 of Texts in Applied Mathematics, 2nd edn. Springer–Verlag, New York (2004). [Google Scholar]
  40. J.A. Sethian, Level set methods and fast marching methods. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. Vol. 3 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge, second edition (1999). [Google Scholar]
  41. J. Sokołowski and J.-P. Zolésio, Introduction to shape optimization. Shape sensitivity analysis. Vol. 16 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (1992). [Google Scholar]
  42. K. Sturm, Minimax Lagrangian approach to the differentiability of non-linear PDE constrained shape functions without saddle point assumption. SIAM J. Control Optim. 53 (2015) 2017–2039. [CrossRef] [MathSciNet] [Google Scholar]
  43. K. Sturm, D. Hömberg and M. Hintermüller, Shape optimization for a sharp interface model of distortion compensation. WIAS-preprint 4 (2013) 807–822. [Google Scholar]
  44. J.-P. Zolésio, Identification de domaines par déformations. Thèse de doctorat d’état, Université de Nice, France (1979). [Google Scholar]

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