Open Access
Issue |
RAIRO-Oper. Res.
Volume 56, Number 5, September-October 2022
|
|
---|---|---|
Page(s) | 3689 - 3709 | |
DOI | https://doi.org/10.1051/ro/2022168 | |
Published online | 31 October 2022 |
- L. Afraites, A new coupled complex boundary method (ccbm) for an inverse obstacle problem. Discrete Contin. Dyn. Syst.-S 15 (2022) 23. [CrossRef] [MathSciNet] [Google Scholar]
- L. Afraites and A. Atlas, Parameters identification in the mathematical model of immune competition cells. J. Inverse Ill-Posed Probl. 23 (2015) 323–337. [CrossRef] [MathSciNet] [Google Scholar]
- L. Afraites, M. Dambrine, K. Eppler and D. Kateb, Detecting perfectly insulated obstacles by shape optimization techniques of order two. Discrete Contin. Dyn. Syst.-B 8 (2007) 389. [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. [CrossRef] [MathSciNet] [Google Scholar]
- L. Afraites, C. Masnaoui and M. Nachaoui, Shape optimization method for an inverse geometric source problem and stability at critical shape. Discrete Contin. Dyn. Syst.-S 15 (2022) 1. [CrossRef] [MathSciNet] [Google Scholar]
- C.J.S. Alves, R. Mamud, N.F.M. Martins and N.C. Roberty, On inverse problems for characteristic sources in helmholtz equations. Math. Probl. Eng. 2017 (2017). [Google Scholar]
- H. Azegami and K. Takeuchi, A smoothing method for shape optimization: traction method using the robin condition. Int. J. Comput. Methods 3 (2006) 21–33. [CrossRef] [Google Scholar]
- F. Caubet, M. Dambrine, D. Kateb and C.Z. Timimoun, A kohn-vogelius formulation to detect an obstacle immersed in a fluid. Inverse Probl. Imaging 7 (2013) 123. [CrossRef] [MathSciNet] [Google Scholar]
- X. Cheng, R. Gong, W. Han and X. Zheng, A novel coupled complex boundary method for solving inverse source problems. Inverse Probl. 30 (2014) 055002. [CrossRef] [Google Scholar]
- P.J. Daniell, Lectures on cauchy’s problem in linear partial differential equations. Math. Gaz. 12 (1924) 173–174. [CrossRef] [Google Scholar]
- R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology: Volume 3 Spectral Theory and Applications, Vol. 3. Springer Science & Business Media (1999). [Google Scholar]
- M.C. Delfour and J.-P. Zolésio, Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization. SIAM (2011). [Google Scholar]
- A. El Badia and T.H. Duong, Some remarks on the problem of source identification from boundary measurements. Inverse Probl. 14 (1998) 883. [CrossRef] [Google Scholar]
- A. El Badia and T. Nara, An inverse source problem for helmholtz’s equation from the cauchy data with a single wave number. Inverse Probl. 27 (2011) 105001. [CrossRef] [Google Scholar]
- K. Eppler and H. Harbrecht, A regularized newton method in electrical impedance tomography using shape hessian information. Control Cybern. 34 (2005) 203. [Google Scholar]
- M. Giacomini, O. Pantz and K. Trabelsi, Certified descent algorithm for shape optimization driven by fully-computable a posteriori error estimators. ESAIM: Control Optim. Calc. Var. 23 (2017) 977–1001. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- R. Gong, X. Cheng and W. Han, A coupled complex boundary method for an inverse conductivity problem with one measurement. Appl. Anal. 96 (2017) 869–885. [CrossRef] [MathSciNet] [Google Scholar]
- J. Haslinger and R.A.E. Mäkinen, Introduction to Shape Optimization: Theory, Approximation, and Computation. SIAM, 2003. [CrossRef] [Google Scholar]
- F. Hecht, Finite Element Library Freefem++. [Google Scholar]
- M. Hrizi and M. Hassine, One-iteration reconstruction algorithm for geometric inverse source problem. J. Elliptic Parabol. Equ. 4 (2018) 177–205. [CrossRef] [MathSciNet] [Google Scholar]
- R. Kress and W. Rundell, A nonlinear integral equation and an iterative algorithm for an inverse source problem. J. Integral Equ. Appl. 27 (2015) 179–198. [CrossRef] [Google Scholar]
- V. Michel and A.S. Fokas, A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet-based methods. Inverse Probl. 24 (2008) 045019. [CrossRef] [Google Scholar]
- F. Murat and J. Simon, Sur le contrôle par un domaine géométrique. Rapport du LA 189 (1976) 76015. [Google Scholar]
- A. Oulmelk, L. Afraites, A. Hadri and M. Nachaoui, An optimal control approach for determining the source term in fractional diffusion equation by different cost functionals. Appl. Numer. Math. 181 (2022) 647–664. [CrossRef] [MathSciNet] [Google Scholar]
- M. Pierre and A. Henrot, Shape Variation and Optimization: A Geometrical Analysis (2018). [Google Scholar]
- J.F.T. Rabago, On the new coupled complex boundary method in shape optimization framework for solving stationary free boundary problems. Preprint arXiv:2205.12620 (2022). [Google Scholar]
- N.C. Roberty and C.J.S. Alves, On the identification of star-shape sources from boundary measurements using a reciprocity functional. Inverse Probl. Sci. Eng. 17 (2009) 187–202. [CrossRef] [MathSciNet] [Google Scholar]
- J.-P. Zolésio and M.C. Delfour, Shapes and Geometries: Analysis, Differential Calculus, and Optimization. SIAM (2001). [Google Scholar]
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