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Inverse Problems in Science and Engineering Volume 21, 2013 - Issue 2
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Original Articles

Application of the linear sampling method to identify cracks with impedance boundary conditions

Fahmi Ben HassenENIT-LAMSIN, Université de Tunis el-Manar, BP 37, 1002 Tunis, Tunisia
,
Yosra BoukariENIT-LAMSIN, Université de Tunis el-Manar, BP 37, 1002 Tunis, Tunisia;INRIA Saclay Ile de France/CMAP Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France
&
Houssem HaddarINRIA Saclay Ile de France/CMAP Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France
Pages 210-234 | Received 15 Jun 2011, Accepted 17 Apr 2012, Published online: 19 Jun 2012

References

  • Cakoni, F, and Colton, D, 2003. The linear sampling method for cracks, Inverse Probl. 19 (2003), pp. 279–295.
  • Delbary, F, , Identifications de fissures par des ondes acoustiques, Ph.D. diss. Université de Paris 6, 2006.
  • Kirsch, A, and Ritter, S, 2000. A linear sampling method for inverse scattering from an open arc, Inverse Probl. 16 (2000), pp. 89–105.
  • Zeev, N, and Cakoni, F, 2009. The identification of thin dielectric objects from far-field or near field scattering data, SIAM J. Appl. Math. 69 (2009), pp. 1024–1042.
  • Zeev, N, 2011. Identification of surface impedance of thin dielectric objects from far-field data, Inverse Probl. 27 (2011), p. 025011.
  • Kress, R, and Lee, KM, 2003. Integral equation methods for scattering from an impedance crack, J. Comput. Appl. Math. 161 (2003), pp. 161–177.
  • Liu, JJ, and Sini, M, 2010. Reconstruction of cracks of different types from far-field measurements, Math. Meth. Appl. Sci. 33 (2010), pp. 950–973.
  • Cakoni, F, and Colton, D, 2003. The determination of the surface impedance of a partially coated obstacle from far-field data, SIAM J. Appl. Math. 2 (2003), pp. 709–723.
  • Ivanyshyn, O, and Kress, R, 2011. Inverse scattering for surface impedance from phase-less far-field data, J. Comput. Phys. 9 (2011), pp. 3443–3452.
  • Kirsch, A, and Grinberg, N, 2008. The Factorization Method for Inverse Problem, Oxford Lecture Series in Mathematics and its Applications, Vol. 36. Oxford: Oxford University Press; 2008.
  • McLean, W, 2000. Strongly Elliptic Systems and Boundary Integral Equations. Cambridge: Cambridge University Press; 2000.
  • Hassen, FBen, Boukari, Y, and Haddar, H, , Application of the linear sampling method to retrieve cracks with impedance boundary conditions, Tech. Rep. INRIA 7478, 2010; available at http://hal.archives-ouvertes.fr/inria-00543901/PDF/RR-7478.pdf.
  • Colton, D, and Kress, R, 1998. Inverse Acoustic and Electromagnetic Scattering Theory, Applied Mathematical Sciences. Vol. 93. Berlin: Springer-Verlag; 1998.
  • Cakoni, F, and Colton, D, 2006. Qualitative Methods in Inverse Scattering Theory. Berlin: Springer-Verlag; 2006.

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