Open Access
Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 85 | |
Number of page(s) | 37 | |
DOI | https://doi.org/10.1051/cocv/2024072 | |
Published online | 08 November 2024 |
- M. Choulli, Some stability inequalities for hybrid inverse problems. Comptes Rendus Math. Acad. Sci. Paris 359 (2021) 1251–1265. [Google Scholar]
- D.-H. Chen, D. Jiang and J. Zou, Convergence rates of Tikhonov regularizations for elliptic and parabolic inverse radiativity problems. Inverse Probl. 36 (2020) 075001, 21. [Google Scholar]
- M. Yamamoto and J. Zou, Simultaneous reconstruction of the initial temperature and heat radiative coefficient. Inverse Probl. 17 (2001) 1181–1202. [CrossRef] [Google Scholar]
- D.N. Hào and T.N.T. Quyen, Convergence rates for Tikhonov regularization of coefficient identification problems in Laplace-type equations. Inverse Probl. 26 (2010) 125014, 23. [Google Scholar]
- H.W. Engl, K. Kunisch and A. Neubauer, Convergence rates for Tikhonov regularisation of nonlinear ill-posed problems. Inverse Probl. 5 (1989) 523–540. [CrossRef] [Google Scholar]
- B. Jin, X. Lu, Q. Quan and Z. Zhou, Convergence rate analysis of Galerkin approximation of inverse potential problem. Inverse Probl. 39 (2023) 015008, 26. [Google Scholar]
- E. Beretta, M.V. de Hoop, E. Francini and S. Vessella, Stable determination of polyhedral interfaces from boundary data for the Helmholtz equation. Commun. Part. Differ. Equ. 40 (2015) 1365–1392. [CrossRef] [Google Scholar]
- E. Beretta and C. Cavaterra, Identifying a space dependent coefficient in a reaction-diffusion equation. Inverse Probl. Imag. 5 (2011) 285–296. [CrossRef] [Google Scholar]
- B. Jin and Z. Zhou, An inverse potential problem for subdiffusion: stability and reconstruction. Inverse Probl. 37 (2021) 015006, 26. [Google Scholar]
- A. Canelas, A. Laurain and A.A. Novotny, A new reconstruction method for the inverse potential problem. J. Computat. Phys. 268 (2014) 417–431. [CrossRef] [Google Scholar]
- A. Canelas, A. Laurain and A.A. Novotny, A new reconstruction method for the inverse source problem from partial boundary measurements. Inverse Probl. 31 (2015) 075009, 24. [CrossRef] [Google Scholar]
- F. Hettlich and W. Rundell, Iterative methods for the reconstruction of an inverse potential problem. Inverse Probl. 12 (1996) 251–266. [CrossRef] [Google Scholar]
- M. Bachmayr and M. Burger, Iterative total variation schemes for nonlinear inverse problems. Inverse Probl. 25 (2009): 105004, 26. [CrossRef] [Google Scholar]
- A. Hauptmann, M. Santacesaria and S. Siltanen, Direct inversion from partial-boundary data in electrical impedance tomography. Inverse Probl. 33 (2017) 025009, 26. [Google Scholar]
- H. Ammari and H. Kang, Reconstruction of small inhomogeneities from boundary measurements. Vol. 1846 of Lecture Notes in Mathematics. Springer-Verlag, Berlin (2004). [Google Scholar]
- B. Harrach and M. Ullrich, Monotonicity-based shape reconstruction in electrical impedance tomography. SIAM J. Math. Anal. 45 (2013) 3382–3403. [CrossRef] [MathSciNet] [Google Scholar]
- H. Ammari, J. Garnier, V. Jugnon and H. Kang, Stability and resolution analysis for a topological derivative based imaging functional. SIAM J. Control Optim. 50 (2012) 48–76. [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]
- Y.F. Albuquerque, A. Laurain and K. Sturm, A shape optimization approach for electrical impedance tomography with point measurements. Inverse Probl. 36 (2020) 095006, 27. [CrossRef] [Google Scholar]
- A. Laurain and K. Sturm, Distributed shape derivative via averaged adjoint method and applications. ESAIM Math. Model. Numer. Anal. 50 (2016) 1241–1267. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- E. Beretta, S. Micheletti, S. Perotto and M. Santacesaria, Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT. J. Computat. Phys. 353 (2008) 264–280. [Google Scholar]
- M.C. Delfour and J.-P. Zolésio, Shapes and geometries. Vol. 22 of Advances in Design and Control, 2nd edn. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2011). [Google Scholar]
- J. Sokolowski and J.-P. Zolésio. Introduction to shape optimization. Vol. 16 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (1992). [Google Scholar]
- D. Liu, A.K. Khambampati, S. Kim and K.Y. Kim, Multi-phase flow monitoring with electrical impedance tomography using level set based method. Nucl. Eng. Des. 289 (2015) 108–116. [CrossRef] [Google Scholar]
- L.A. Vese and T.F. Chan, A multiphase level set framework for image segmentation using the mumford and shah model. Int. J. Comput. Vis. 50 (2002) 271–293. Cited by: 2249. [CrossRef] [Google Scholar]
- D. Liu and J. Du, Shape and topology optimization in electrical impedance tomography via moving morphable components method. Struct. Multidiscipl. Optim. 64 (2021) 585–598. [CrossRef] [Google Scholar]
- D.P. Bourne, A.J. Mulholland, S. Sahu and K.M.M. Tant, An inverse problem for Voronoi diagrams: a simplified model of non-destructive testing with ultrasonic arrays. Math. Methods Appl. Sci. 44 (2021) 3727–3745. [CrossRef] [MathSciNet] [Google Scholar]
- P.F. Ash and E.D. Bolker, Recognizing Dirichlet tessellations. Geom. Dedicata 19 (1985) 175–206. [MathSciNet] [Google Scholar]
- A. Suzuki and M. Iri, Approximation of a tessellation of the plane by a Voronoi diagram. J. Oper. Res. Soc. Japan 29 (1986) 69–97. [MathSciNet] [Google Scholar]
- E.G. Birgin, A. Laurain and T.C. Menezes, Sensitivity analysis and tailored design of minimization diagrams. Math. Computat. 92 (2023) 2715–2768. [CrossRef] [Google Scholar]
- A. Laurain, Distributed and boundary expressions of first and second order shape derivatives in nonsmooth domains. J. Math. Pures Appl. 134 (2020) 328–368. [CrossRef] [MathSciNet] [Google Scholar]
- E.G. Birgin, A. Laurain, R. Massambone and A.G. Santana, A shape optimization approach to the problem of covering a two-dimensional region with minimum-radius identical balls. SIAM J. Sci. Comput. 43 (2021) A2047–A2078. [CrossRef] [Google Scholar]
- E.G. Birgin, A. Laurain, R. Massambone and A.G. Santana, A shape-Newton approach to the problem of covering with identical balls. SIAM J. Sci. Comput. 44 (2022) A798–A824. [CrossRef] [Google Scholar]
- R. Hiptmair, A. Paganini and S. Sargheini, Comparison of approximate shape gradients. BIT 55 (2015) 459–485. [CrossRef] [MathSciNet] [Google Scholar]
- A. Laurain, A level set-based structural optimization code using FEniCS. Struct. Multidiscipl. Optim. 58 (2018) 1311–1334. [CrossRef] [Google Scholar]
- S. Zhu, Effective shape optimization of Laplace eigenvalue problems using domain expressions of Eulerian derivatives. J. Optim. Theory Appl. 176 (2018) 17–34. [CrossRef] [MathSciNet] [Google Scholar]
- K. Sturm, Minimax Lagrangian approach to the differentiability of nonlinear PDE constrained shape functions without saddle point assumption. SIAM J. Control Optim. 53 (2015) 2017–2039. [CrossRef] [MathSciNet] [Google Scholar]
- P. Grisvard, Elliptic problems in nonsmooth domains. Vol. 24 of Monographs and Studies in Mathematics. Pitman (Advanced Publishing Program), Boston, MA (1985). [Google Scholar]
- P. Domenico Lamberti and L. Provenzano, On trace theorems for Sobolev spaces. Matematiche (Catania) 75 (2020) 137–165. [MathSciNet] [Google Scholar]
- D.P. Bertsekas, On the goldstein-levitin-polyak gradient projection method. IEEE Trans. Automatic Control 21 (1976) 174–184. [CrossRef] [MathSciNet] [Google Scholar]
- A.A. Goldstein, Convex programming in Hilbert space. Bull. Am. Math. Soc. 70 (1964) 709–710. [CrossRef] [Google Scholar]
- E.S. Levitin and B.T. Polyak, Constrained minimization methods. USSR Computat. Math. Math. Phys. 6 (1966) 1–50. [CrossRef] [Google Scholar]
- H.P. Langtangen and A. Logg, Solving PDEs in Python: The FEniCS Tutorial I. Simula SpringerBriefs on Computing. Springer International Publishing (2017). [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]
- E.G. Birgin, J.M. Martínez and M. Raydan, Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10 (2000) 1196–1211. [CrossRef] [MathSciNet] [Google Scholar]
- E.G. Birgin, J.M. Martínez and M. Raydan, Algorithm 813: SPG—software for convex-constrained optimization. ACM Trans. Math. Softw. 27 (2001) 340–349. [CrossRef] [Google Scholar]
- J. Barzilai and J.M. Borwein, Two-point step size gradient methods. IMA J. Numer. Anal. 8 (1988) 141–148. [CrossRef] [MathSciNet] [Google Scholar]
- M. Raydan, On the Barzilai and Borwein choice of steplength for the gradient method. IMA J. Numer. Anal. 13 (1993) 321–326. [CrossRef] [MathSciNet] [Google Scholar]
- M. Raydan, The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J. Optim. 7 (1997) 26–33. [Google Scholar]
- L. Grippo, F. Lampariello and S. Lucidi, A nonmonotone line search technique for Newton’s method. SIAM J. Numer. Anal. 23 (1986) 707–716. [Google Scholar]
- E.G. Birgin, A. Laurain and D.R. Souza, FEniCS code for “Reconstruction of Voronoi diagrams in inverse potential problems”. https://github.com/Souza-DR/bls2024-potential (2024). [Google Scholar]
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