Publication Cover
Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 5
191
Views
25
CrossRef citations to date
0
Altmetric
Articles

The inverse scattering problem for a partially coated cavity with interior measurements

, &
Pages 936-956 | Received 22 Jan 2013, Accepted 29 Apr 2013, Published online: 18 Jun 2013

References

  • Cakoni F, Colton D. Qualitative methods in inverse scattering theory. Berlin: Springer; 2006.
  • Cakoni F, Colton D, Monk P. The linear sampling method in inverse electromagnetic scattering, CBMS Series, Vol. 80. SIAM Publications; 2011.
  • Kirsch A, Grinberg N. The factorization method for inverse problems. New York: Oxford University Press; 2008.
  • Potthast R. A point source method for inverse acoustic and electromagnetic obstacle scattering problems. IMA Journal of Applied Mathematics. 1998;61(2):119–140.
  • Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. New York: Springer; 2013.
  • Cakoni F, Colton D, Monk P. The direct and inverse scattering problems for partially coated obstacles. Inverse Problems. 2001;17:1997–2015.
  • Cakoni F, Colton D. The determination of the surface impedance of a partially coated obstacle from far field data. SIAM Journal on Applied Mathematics. 2004;64:709–723.
  • Cakoni F, Colton D, Monk P. The determination of the surface conductivity of a partially coated dielectric. SIAM Journal on Applied Mathematics. 2005;65:767–789.
  • Cakoni F, Kress R, Schuft C. Integral equations for shape and impedance reconstruction in corrosion detection. Inverse Problems. 2010; 26(9) [paper 095012].
  • Liu JJ, Nakamura G, Sini M. Reconstruction of the shape and surface impedance for acoustic scattering data for an arbitrary cylinder. SIAM Journal on Applied Mathematics. 2007;67(4):1124–1146.
  • Wang HB, Liu JJ. On the reconstruction of surface impedance from the far-field data in inverse scattering problems. Applicable Analysis. 2012;91(4):787–806.
  • Qin HH, Colton D. The inverse scattering problem for cavities with impedance boundary condition. Journal of Advances in Computational Mathematics. 2012;36(2):157–174.
  • Qin HH, Colton D. The inverse scattering problem for cavities. Journal of Applied Numerical Mathematics. 2012;62:699–708.
  • Zeng F, Cakoni F, Sun J. An inverse electromagnetic scattering problem for cavity. Inverse Problems. 2011;27(12):125002.
  • Qin HH, Cakoni F. Nonlinear integral equations for shape reconstruction in the inverse interior scattering problem. Inverse Problems. 2011;27(3):035005.
  • Ikehata M, Itou H. On reconstruction of a cavity in a linearized viscoelastic body from infinitely many transient boundary data. Inverse Problems. 2012;28:125003.
  • Ikehata M, Itou H. An inverse acoustic scattering problem inside a cavity with dynamical back-scattering data. Inverse Problems. 2012;28:095016.
  • Jakubik P. esting the integrity of some cavity-the Cauchy problem and the range test. Applied Numerical Mathematics. 2008;58:899–914.
  • Nakamura G, Sini M. Obstacle and boundary determination from scattering data. SIAM Journal on Mathematical Analysis. 2007;39:819–837.
  • McLean W. Strongly elliptic systems and boundary integral equations. Cambridge: Cambridge University Press; 2000.
  • Kress R. Linear integral equations. Berlin: Springer-Verlag; 1989.
  • Arens T. Why linear sampling works. Inverse Problems. 2004;20(1):163–173.
  • Arens T, Lechleiter A. The linear sampling method revisited. Journal of Integral Equations and Applications. 2009;21(2):179–202.
  • Collino F, Fares MB, Haddar H. Numerical and analytical studies of the linear sampling method in electromagnetic inverse scattering problems. Inverse Problems. 2003;19(6):1279–1298.
  • Li JZh. Strengthened linear sampling method with a reference ball. SIAM Journal on Applied Mathematics. 2009;31(6):4013–4040.
  • Colton D, Kress R. Eigenvalues of the far field operator and inverse scattering theory. SIAM Journal on Mathematical Analysis. 1995;26:601–615.
  • Kreyszig E. Introductory functional analysis with applications. New York: John Wiley; 1978.
  • Hadamard J. Lectures on Cauchy’s Problem in Linear Partial Differential Equations. New York: Dover Publications; 1953.
  • Kirsch A. An introduction to the mathematical theory of inverse problems. Berlin: Springer; 1996.
  • Hansen PC. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Review. 1992;34:561–580.
  • Hansen PC. Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems. Numerical Algorithms. 1994;6:1–35.
  • Cakoni F, Monk P. The determination of anisotropic surface impedance in electromagnetic scattering. Journal on Methods and Applications of Analysis. 2010;17(4):379–394.
  • Liu JJ, Sini M. On the accuracy of the numerical detection of complex obstacles from far field data using the probe method. SIAM J. Sci. Comput. 2009;31(4):2665–2687.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.