Cakoni, Fioralba; Colton, David; Haddar, Houssem The linear sampling method for anisotropic media. (English) Zbl 1019.78003 J. Comput. Appl. Math. 146, No. 2, 285-299 (2002). The authors present an analysis of the linear sampling method to determine the support of an anisotropic inhomogeneous penetrable scatterer from a knowledge of the incident and scattered time harmonic acoustic wave at fixed frequency. They extend the results of D. Colton, R. Kress and P. Monk [J. Comput. Appl. Math. 81, 269-298 (1997; Zbl 0885.35143)] to the case of (possibly) complex-valued anisotropic medium that does not vary smoothly across the boundary. The method is based on an analysis of the interior transmission problem, and the paper also gives appropriate conditions under which the set of transmission eigenvalues is discrete. Reviewer: Johannes Elschner (Berlin) Cited in 1 ReviewCited in 26 Documents MSC: 78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory 35R30 Inverse problems for PDEs 35P25 Scattering theory for PDEs Keywords:inverse scattering; anisotropic medium; linear sampling method; interior transmission problem Citations:Zbl 0885.35143 PDFBibTeX XMLCite \textit{F. Cakoni} et al., J. Comput. Appl. Math. 146, No. 2, 285--299 (2002; Zbl 1019.78003) Full Text: DOI References: [1] Colton, D.; Coyle, J.; Monk, P., Recent developments in inverse acoustic scattering theory, SIAM Rev., 42, 3, 369-414 (2000) · Zbl 0960.76081 [2] Colton, D.; Kress, R., Inverse Acoustic and Electromagnetic Scattering Theory (1998), Springer: Springer Berlin · Zbl 0893.35138 [3] Colton, D.; Kress, R.; Monk, P., Inverse scattering from an orthotropic medium, J. Comput. Appl. Math., 81, 269-298 (1997) · Zbl 0885.35143 [4] Colton, D.; Päivärinta, L., Transmission eigenvalues and a problem of Hans Lewy, J. Comput. Appl. Math., 117, 91-104 (2000) · Zbl 0957.65093 [5] Colton, D.; Potthast, R., The inverse electromagnetic scattering problem for an anisotropic medium, Quart. J. Mech. Appl. Math., 52, 349-372 (1999) · Zbl 0967.78006 [6] Colton, D.; Sleeman, B., An approximation property of importance in inverse scattering theory, Proc. Edinburgh Math. Soc., 44, 449-454 (2001) · Zbl 0992.35115 [7] Coyle, J., An inverse electromagnetic scattering problem in a two-layered background, Inverse Problems, 16, 275-292 (2000) · Zbl 0973.35196 [8] Gylys-Colwell, F., An inverse problem for the Helmholtz equation, Inverse Problems, 16, 139-156 (2000) · Zbl 0860.35142 [9] Hähner, P., On the uniqueness of the shape of a penetrable, anisotropic obstacle, J. Comput. Appl. Math., 116, 167-180 (2000) · Zbl 0978.35098 [10] Hörmander, L., The Analysis of Linear differential Operators, Vol. 3 (1985), Springer: Springer Berlin [11] Kirsch, A., Factorization of the far field operator for the inhomogeneous medium case and an application in inverse scattering theory, Inverse Problems, 15, 413-429 (1999) · Zbl 0926.35162 [12] Piana, M., On the uniqueness for anisotropic inhomogeneous inverse scattering problems, Inverse Problems, 14, 1565-1579 (1998) · Zbl 0920.35170 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.