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 |
- 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]
- 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]
- 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]
- 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]
- L. Borcea, Electrical impedance tomography. Inverse Problems 18 (2002) R99–R136. [CrossRef] [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- M. Cheney, D. Isaacson and J.C. Newell, Electrical impedance tomography. SIAM Rev. 41 (1999) 85–101 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- F. Hettlich, The domain derivative of time-harmonic electromagnetic waves at interfaces. Math. Methods Appl. Sci. 35 (2012) 1681–1689. [CrossRef] [MathSciNet] [Google Scholar]
- M. Hintermüller and A. Laurain, Electrical impedance tomography: from topology to shape. Control Cybernet. 37 (2008) 913–933. [MathSciNet] [Google Scholar]
- 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]
- 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]
- M. Hintermüller, A. Laurain and A.A. Novotny, Second-order topological expansion for electrical impedance tomography. Adv. Comput. Math. (2011) 1–31. [Google Scholar]
- 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]
- R. Hiptmair, A. Paganini and S. Sargheini, Comparison of approximate shape gradients. BIT 55 (2015) 459–485. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- R. Kress, Inverse problems and conformal mapping. Complex Var. Elliptic Equ. 57 (2012) 301–316. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- 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]
- M. Nagumo, Über die Lage der Integralkurven gewöhnlicher Differentialgleichungen. Proc. Phys. Math. Soc. Japan 24 (1942) 551–559. [MathSciNet] [Google Scholar]
- A.A. Novotny and J. Sokołowski, Topological derivatives in shape optimization. Interaction of Mechanics and Mathematics. Springer, Heidelberg (2013). [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- J.-P. Zolésio, Identification de domaines par déformations. Thèse de doctorat d’état, Université de Nice, France (1979). [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.