86
Views
4
CrossRef citations to date
0
Altmetric
Articles

The inside–outside duality for elastic scattering problems

Pages 48-69 | Received 09 Mar 2016, Accepted 03 Jul 2016, Published online: 25 Jul 2016

References

  • Arens T. Linear sampling methods for 2d inverse elastic wave scattering. Inverse Prob. 2001;17:1445–1464.
  • Alves CJS, Kress R. On the far-field operator in elastic obstacle scattering. IMA J. Appl. Math. 2002;67:1–21.
  • Hu G, Kirsch A, Sini M. Some inverse problems arising from elastic scattering by rigid obstacles. Inverse Prob. 2013;29:015009, 21.
  • McLean W. Strongly elliptic systems and boundary integral operators. Cambridge: Cambridge University Press; 2000.
  • Lechleiter A, Peters S. Analytical characterization and numerical approximation of interior eigenvalues for impenetrable scatterers from far fields. Inverse Prob. 2014;30:045006.
  • Charalambopoulos A. On the interior transmission problem in nondissipative, inhomogeneous, anisotropic elasticity. J. Elast. 2002;67:149–170.
  • Charalambopoulos A, Anagnostopoulos K. On the spectrum of the interior transmission problem in isotropic elasticity. J. Elast. 2008;90:295–313.
  • Bellis C, Guzina B. On the existence and uniqueness of a solution to the interior transmission problem for piecewise-homogeneous solids. J. Elast. 2010;101:29–57.
  • Bellis C, Cakoni F, Guzina B. Nature of the transmission eigenvalue spectrum for elastic bodies. IMA J. Appl. Math. 2013;78:895–923.
  • Charalambopoulos A, Gintides D, Kiriaki K. The linear sampling method for the transmission problem in three-dimensional linear elasticity. Inverse Prob. 2002;18:547–558.
  • Baganas K, Guzina B, Charalambopoulos A, et al. A linear sampling method for the inverse transmission problem in near-field elastodynamics. Inverse Prob. 2006;22:1835–1853.
  • Guzina B, Madyarov A. A linear sampling approach to inverse elastic scattering in piecewise-homogeneous domains. Inverse Prob. 2007;23:1467–1493.
  • Charalambopoulos A, Kirsch A, Anagnostopoulos KA, et al. The factorization method in inverse elastic scattering from penetrable bodies. Inverse Prob. 2007;23:27–51.
  • Kirsch A, Lechleiter A. The inside--outside duality for scattering problems by inhomogeneous media. Inverse Prob. 2013;29:104011.
  • Lechleiter A, Peters S. Determining transmission eigenvalues of anisotropic inhomogeneous media from far field data. Commun. Math. Sci. 2015;13:1803–1827.
  • Lechleiter A, Peters S. The inside--outside duality for inverse scattering problems with near field data. Inverse Prob. 2015;31:085004, 23.
  • Peters S, Kleefeld A. Numerical computations of interior transmission eigenvalues for scattering objects with cavities. Inverse Prob. 2016;32:045001.
  • Kupradze VD. Potential methods in the theory of elasticity. Gutfreund H, translator; Meroz I, editor. Israel Program for Scientific Translations, Jerusalem. New York (NY): Daniel Davey & Co., Inc; 1965. Russian.
  • Kupradze VD, Gegelia TG, Basheleuishvili MO, et al. Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. Vol. 25, North-Holland series in applied mathematics and mechanics. Amsterdam: North-Holland Publishing Co.; russian edition, 1979. Edited by V. D. Kupradze.
  • Peter H. A uniqueness theorem in inverse scattering of elastic waves. IMA J. Appl. Math. 1993;51:201–215.
  • Sevroglou V. The far-field operator for penetrable and absorbing obstacles in 2D inverse elastic scattering. Inverse Prob. 2005;21:717–738.
  • Arens T. An approximation property of elastic Herglotz wave functions and its application in the linear sampling method. J. Inverse Ill-Posed Prob. 2003;11:219–233.
  • Hsiao GC, Wendland WL. Boundary integral equations. Vol. 164, Berlin: Springer-Verlag; 2008.
  • Kirsch A. On the existence of transmission eigenvalues. Inverse Prob. Imaging. 2009;3:155–172.
  • Kirsch A, Grinberg NI. The factorization method for inverse problems. Vol. 36, Oxford lecture series in mathematics and its applications. Oxford: Oxford University Press; 2008.

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.