Determining transmission eigenvalues of anisotropic inhomogeneous media from far field data

Communications in Mathematical Sciences

Volumn 13, Issue 7, 2015, Pages 1803-1827

  Lechleiter, Armin ^a   Peters, Stefan ^a  

^a UNIVERSITY OF BREMEN   (Germany)

Author keywords

Anisotropic scattering; Inside outside duality; Transmission eigenvalues

Indexed keywords

EID: 84937915110     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2015.v13.n7.a8     Document Type: Article

References (24)

1. F. Cakoni and D. Colton, A uniqueness theorem for an inverse electromagnetic scattering problem in inhomogeneous anisotropic media, Proc. Edinburgh. Math. Soc., 46, 293-314, 2003.
2. F. Cakoni and D. Colton, Qualitative Methods in Inverse Scattering Theory. An Introduction, Springer, Berlin, 2006.
3. F. Cakoni, D. Colton, and H. Haddar, The computation of lower bounds for the norm of the index of refraction in an anisotropic madia, J. Int. Equ. Appl., 21, 203-227, 2009.
4. F. Cakoni, D. Colton, and H. Haddar, On the determination of Dirichlet and transmission eigenvalues from far field data, C.R. Math. Acad. Sci. Paris, Ser. I, 348, 379-383, 2010.
5. F. Cakoni, D. Colton, and P. Monk, On the use of transmission eigenvalues to estimate the index of refraction from far field data, Inverse Problems, 23, 507-522, 2007.
6. F. Cakoni, D. Colton, and P. Monk, The linear sampling method in inverse electromagnetic scattering, SIAM, Philadelphia, 2011.
7. F. Cakoni, D. Colton, P. Monk, and J. Sun, The inverse electromagnetic scattering problem for anisotropic media, Inverse Problems, 26, 074004, 2010.
8. F. Cakoni and H. Haddar, Transmission eigenvalues in inverse scattering theory, 60, 529-580, 2013.
9. D.L. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, Third Edition, 2013.
10. J.-P. Eckmann and C.-A. Pillet, Spectral duality for planar billiards, Commun. Math. Phys., 283-313, 1995.
11. F. Gazzola, H.-C. Grunau, and G. Sweers, Polyharmonic Boundary Value Problems, in Lecture Notes in Mathematics, Springer, New York, 1991, 2013.
12. F. Gylys-Colwell, An inverse problem for the Helmholtz equation, Inverse Probl., 12, 139-156, 1996.
13. Z. Jiang and A. Lechleiter, Computing interior eigenvalue from far fields, in preparation, 2014.
14. A. Kirsch and N.I. Grinberg, The Factorization Method for Inverse Problems, Oxford Lecture Series Math. Appl., Oxford University Press, 36, 2008.
15. A. Kirsch and A. Lechleiter, inside-outside duality for scattering problems by inhomogeneous media, Inverse Problems, 29(10), 104011, 2013.
16. A. Kirsch, An integral equation for the scattering problem for an anisotropic medium and the factorization method, World Sci. Publ., Hackensack, NJ, Advanced topics in scattering and biomedical engineering, 57-70, 2008.
17. A. Kirsch, On the existence of transmission eigenvalues, Inverse Probl. Imaging, 3, 155-172, 2009.
18. R.E. Kleinman and P.A. Martin, On single integral equations for the transmission problem of acoustics, SIAM J. Appl. Math., 48, 307-325, 1988.
19. A. Lechleiter and S. Peters, Analytical characterization and numerical approximation of interior eigenvalues for impenetrable scatterers from far fields, Inverse Problems, 30(4), 045006, 2014.
20. W. McLean, Strongly Elliptic Systems and Boundary Integral Operators, Cambridge University Press, Cambridge, UK, 2000.
21. P. Monk, Finite Element Methods for Maxwell's Equations, Oxford Science Publications, Oxford, 2003.
22. J.-C. Nédélec, Acoustic and Electromagnetic Equations, Springer, New York, 2001.
23. M. Piana, On the uniqueness for anisotropic inhomogeneous inverse scattering problems, Inverse Problems, 14, 1565-1579, 1998.
24. W. Smigaj, T. Betcke, S. Arridge, J. Phillips, and M. Schweiger, Solving boundary integral problems with BEM++, ACM Trans. Math. Software, 41(2), Art. 6, 2015.