Free Access
Issue
ESAIM: COCV
Volume 23, Number 3, July-September 2017
Page(s) 977 - 1001
DOI https://doi.org/10.1051/cocv/2016021
Published online 28 April 2017
  1. L. Afraites, M. Dambrine and D. Kateb, Shape methods for the transmission problem with a single measurement. Numer. Func. Anal. Opt. 28 (2007) 519–551. [CrossRef] [MathSciNet] [Google Scholar]
  2. L. Afraites, M. Dambrine and D. Kateb, On second order shape optimization methods for electrical impedance tomography. SIAM J. Control Optim. 47 (2008) 1556–1590. [CrossRef] [MathSciNet] [Google Scholar]
  3. F. Alauzet, B. Mohammadi and O. Pironneau, Mesh adaptivity and optimal shape design for aerospace. In Variational Analysis and Aerospace Engineering: Mathematical Challenges for Aerospace Design, edited by G. Buttazzo and A. Frediani. Optimization and Its Applications. Springer US (2012) 323–337. [Google Scholar]
  4. G. Allaire and O. Pantz, Structural optimization with FreeFem++. Struct. Multidisc. Optim. 32 (2006) 173–181. [CrossRef] [Google Scholar]
  5. H. Ammari, E. Bossy, J. Garnier and L. Seppecher, Acousto-electromagnetic tomography. SIAM J. Appl. Math. 72 (2012) 1592–1617. [CrossRef] [MathSciNet] [Google Scholar]
  6. H. Azegami, S. Kaizu, M. Shimoda and E. Katamine, Irregularity of shape optimization problems and an improvement technique. In Computer Aided Optimization Design of Structures V, edited by S. Hernandez and C. Brebbia. Computational Mechanics Publications (1997) 309–326. [Google Scholar]
  7. N. Banichuk, F.-J. Barthold, A. Falk and E. Stein, Mesh refinement for shape optimization. Struct. Optim. 9 (1995) 46–51. [CrossRef] [Google Scholar]
  8. L. Borcea, Electrical impedance tomography. Inverse Probl. 18 (2002) R99. [CrossRef] [Google Scholar]
  9. A. 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. (1980) 65–73. [Google Scholar]
  10. A. Carpio and M.-L. Rapún, Hybrid topological derivative and gradient-based methods for electrical impedance tomography. Inverse Probl. 28 (2012) 095010. [CrossRef] [Google Scholar]
  11. J. Céa, Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût. ESAIM: M2AN 20 (1986) 371–402. [CrossRef] [EDP Sciences] [Google Scholar]
  12. M. Cheney, D. Isaacson and J. Newell, Electrical impedance tomography. SIAM Rev. 41 (1999) 85–101. [CrossRef] [MathSciNet] [Google Scholar]
  13. E. Chung, T. 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]
  14. M. Delfour and J.-P. Zolésio, Shapes and geometries: analysis, differential calculus, and optimization. SIAM, Philadelphia, USA (2001). [Google Scholar]
  15. G. Dogǎn, P. Morin, R. Nochetto and M. Verani, Discrete gradient flows for shape optimization and applications. Special Issue Honoring the 80th Birthday of Professor Ivo Babuka. Comput. Methods Appl. Mech. Engrg. 196 (2007) 3898–3914. [CrossRef] [MathSciNet] [Google Scholar]
  16. K. Eppler and H. Harbrecht, A regularized Newton method in electrical impedance tomography using shape Hessian information. Control Cybernet. 34 (2005) 203–225. [MathSciNet] [Google Scholar]
  17. L. Formaggia, S. Micheletti and S. Perotto, Anisotropic mesh adaption in computational fluid dynamics: application to the advection-diffusion-reaction and the Stokes problems. Appl. Numer. Math. 51 (2004) 511–533. [CrossRef] [MathSciNet] [Google Scholar]
  18. T. Grätsch and K.-J. Bathe, Goal-oriented error estimation in the analysis of fluid flows with structural interactions. Comput. Methods Appl. Mech. Engrg. 195 (2006) 5673–5684. [CrossRef] [MathSciNet] [Google Scholar]
  19. F. Hecht, New development in FreeFem++. J. Numer. Math. 20 (2012) 251–265. [CrossRef] [MathSciNet] [Google Scholar]
  20. M. Hintermüller and A. Laurain, Electrical impedance tomography: from topology to shape. Control Cybern. 37 (2008) 913–933. [Google Scholar]
  21. M. Hintermüller, A. Laurain and A.A. Novotny, Second-order topological expansion for electrical impedance tomography. Adv. Comput. Math. 36 (2012) 235–265. [CrossRef] [MathSciNet] [Google Scholar]
  22. R. Hiptmair, A. Paganini and S. Sargheini, Comparison of approximate shape gradients. BIT Numer. Math. 54 (2014) 1–27. [CrossRef] [Google Scholar]
  23. D. Holder, Electrical Impedance Tomography: Methods, History and Applications. Series in Medical Physics and Biomedical Engineering. CRC Press (2004). [Google Scholar]
  24. B. Jin and P. Maass, An analysis of electrical impedance tomography with applications to Tikhonov regularization. ESAIM: COCV 18 (2012) 1027–1048. [CrossRef] [EDP Sciences] [Google Scholar]
  25. N. Kikuchi, K. Chung, T. Torigaki and J. Taylor, Adaptive Finite Element Methods for shape optimization of linearly elastic structures. Comput. Methods Appl. Mech. Eng. 57 (1986) 67–89. [CrossRef] [Google Scholar]
  26. R. Kohn and M. Vogelius, Relaxation of a variational method for impedance computed tomography. Comm. Pure Appl. Math. 40 (1987) 745–777. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Laurain and K. Sturm, Distributed shape derivative via averaged adjoint method and applications. ESAIM: M2AN 50 (2016) 1241–1267. [CrossRef] [EDP Sciences] [Google Scholar]
  28. P. Morin, R. Nochetto, M. Pauletti and M. Verani, Adaptive finite element method for shape optimization. ESAIM: COCV 18 (2012) 1122–1149. [CrossRef] [EDP Sciences] [Google Scholar]
  29. J. Oden and S. Prudhomme, Goal-oriented error estimation and adaptivity for the Finite Element Method. Comput. Math. Appl. 41 (2001) 735–756. [CrossRef] [MathSciNet] [Google Scholar]
  30. O. Pantz, Sensibilité de l’équation de la chaleur aux sauts de conductivité. C. R. Acad. Sci. Paris, Ser. I (2005) 333–337. [Google Scholar]
  31. G. Porta, S. Perotto and F. Ballio, Anisotropic mesh adaptation driven by a recovery-based error estimator for shallow water flow modeling. Int. J. Numer. Methods Fluids 70 (2012) 269–299. [CrossRef] [Google Scholar]
  32. S. Prudhomme, J. Oden, T. Westermann, J. Bass and M. Botkin, Practical methods for a posteriori error estimation in engineering applications. Int. J. Numer. Methods Engrg. 56 (2003) 1193–1224. [CrossRef] [Google Scholar]
  33. S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comput. 69 (2000) 481–500. [CrossRef] [MathSciNet] [Google Scholar]
  34. J. Roche, Adaptive Newton-like method for shape optimization. Control Cybern. 34 (2005) 363–377. [Google Scholar]
  35. M. Rüter, T. Gerasimov and E. Stein, Goal-oriented explicit residual-type error estimates in XFEM. Comput. Mech. 52 (2013) 361–376. [CrossRef] [MathSciNet] [Google Scholar]
  36. A. Schleupen, K. Maute and E. Ramm, Adaptive FE-procedures in shape optimization. Struct. Multidisc. Optim. 19 (2000) 282–302. [CrossRef] [Google Scholar]
  37. J. Sokołowski and J. Zolésio, Introduction to shape optimization: shape sensitivity analysis. Springer-Verlag (1992). [Google Scholar]
  38. J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem. Ann. Math. 125 (1987) 153–169. [CrossRef] [MathSciNet] [Google Scholar]
  39. T. Vejchodský, Complementary error bounds for elliptic systems and applications. Appl. Math. Comput. 219 (2013) 7194–7205. [MathSciNet] [Google Scholar]
  40. A. Wexler, B. Fry and M.R. Neuman, Impedance-computed tomography algorithm and system. Appl. Opt. 24 (1985) 3985–3992. [CrossRef] [PubMed] [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.