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Inverse Problems and Imaging (IPI)
 

Factorization method in inverse interaction problems with bi-periodic interfaces between acoustic and elastic waves
Pages: 103 - 129, Issue 1, February 2016

doi:10.3934/ipi.2016.10.103      Abstract        References        Full text (2457.4K)           Related Articles

Guanghui Hu - Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany (email)
Andreas Kirsch - Department of Mathematics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany (email)
Tao Yin - College of Mathematics and Statistics, Chongqing University, China (email)

1 T. Arens and N. Grinberg, A complete factorization method for scattering by periodic surface, Computing, 75 (2005), 111-132.       
2 T. Arens and A. Kirsch, The factorization method in inverse scattering from periodic structures, Inverse Problems, 19 (2003), 1195-1211.       
3 A. S. Bonnet-Bendhia and P. Starling, Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem, Math. Meth. Appl. Sci., 17 (1994), 305-338.       
4 P. Carney and J. Schotland, Three-dimensional total internal reflection microscopy, Optics Letters, 26 (2001), 1072-1074.
5 J. M. Claeys, O. Leroy, A. Jungman and L. Adler, Diffraction of ultrasonic waves from periodically rough liquid-solid surface, J. Appl. Phys., 54 (1983), 5657.
6 D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Berlin, Springer, 1998.       
7 D. Courjon and C. Bainier, Near field microscopy and near field optics, Rep. Prog. Phys., 57 (1994), 989-1028.
8 N. F. Declercq, J. Degrieck, R. Briers and O. Leroy, Diffraction of homogeneous and inhomogeneous plane waves on a doubly corrugated liquid/solid interface, Ultrasonics, 43 (2005), 605-618.
9 J. Elschner and G. Hu, Variational approach to scattering of plane elastic waves by diffraction gratings, Math. Meth. Appl. Sci., 33 (2010), 1924-1941.       
10 J. Elschner and G. Hu, Scattering of plane elastic waves by three-dimensional diffraction gratings, Mathematical Models and Methods in Applied Sciences, 22 (2012), 1150019, 34pp.       
11 J. Elschner, G. C. Hsiao and A. Rathsfeld, An inverse problem for fluid-solid interaction, Inverse Problems and Imaging, 2 (2008), 83-119.       
12 J. Elschner, G. C. Hsiao and A. Rathsfeld, An optimization method in inverse acoustic scattering by an elastic obstacle, SIAM J. Appl. Math., 70 (2009), 168-187.       
13 J. Elschner and G. Schmidt, Diffraction in periodic structures and optimal design of binary gratings I. Direct problems and gradient formulas, Math. Meth. Appl. Sci., 21 (1998), 1297-1342.       
14 N. Favretto-Anrès and G. Rabau, Excitation of the Stoneley-Scholte wave at the boundary between an ideal fluid and a viscoelastic solid, Journal of Sound and Vibration, 203 (1997), 193-208.
15 C. Girard and A. Dereux, Near-field optics theories, Rep. Prog. Phys., 59 (1996), 657-699.
16 F. Hettlich and A. Kirsch, Schiffer's theorem in inverse scattering for periodic structures, Inverse Problems, 13 (1997), 351-361.       
17 G. C. Hsiao, R. E. Kleinman and G. F. Roach, Weak solution of fluid-solid interaction problem, Math. Nachr., 218 (2000), 139-163.       
18 G. Hu, Y. L. Lu and B. Zhang, The factorization method for inverse elastic scattering from periodic structures, Inverse Problems, 29 (2013), 115005, 25pp.       
19 G. Hu, J. Yang, B. Zhang and H. Zhang, Near-field imaging of scattering obstacles with the factorization method, Inverse Problems, 30 (2014), 095005, 25pp.       
20 G. Hu, A. Rathsfeld and T. Yin, Finite element method for fluid-solid interaction problem with unbounded perioidc interfaces, Numerical Methods for Partial Differential Equations, 32 (2016), 5-35.
21 S. W. Herbison, Ultrasonic Diffraction Effects on Periodic Surfaces, Georgia Institute of Technology, PhD Thesis, 2011.
22 A. Kirsch, Characterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems, 14 (1998), 1489-1512.       
23 A. Kirsch, Diffraction by periodic structures, in Proc. Lapland Conf. Inverse Problems, (eds. L. Päivärinta et al), Berlin, Springer, 422 (1993), 87-102.       
24 A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, New York, Oxford Univ. Press, 2008.       
25 A. Kirsch and A. Ruiz, The factorization method for an inverse fluid-solid interaction scattering problem, Inverse Problems and Imaging, 6 (2012), 681-695.       
26 V. D. Kupradze, et al., Three-dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, Amsterdam, North-Holland, 1979.       
27 A. Lechleiter, Factorization Methods for Photonics and Rough Surfaces, PhD thesis, University of Karlsruhe, 2008.
28 A. Lechleiter and D. L. Nguyen, Factorization method for electromagnetic inverse scattering from biperiodic structures, SIAM Journal on Imaging Sciences, 6 (2013), 1111-1139.       
29 C. J. Luke and P. A. Martin, Fluid-solid interaction: Acoustic scattering by a smooth elastic obstacle, SIAM J. Appl. Math., 55 (1995), 904-922.       
30 K. Mampaert and O. Leroy, Reflection and transmission of normally incident ultasonic waves on periodic solid-liquid interfaces, J. Acoust. Soc. Amer., 83 (1988), 1390-1398.
31 P. Monk and V. Selgas, An inverse fluid-solid interaction problem, Inverse Probl. Imaging, 3 (2009), 173-198.       
32 P. Monk and V. Selgas, Near field sampling type methods for the inverse fluid-solid interaction problem, Inverse Probl. Imaging, 5 (2011), 465-483.       

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