Nearfield imaging of soundsoft obstacles in periodic waveguides
Pages: 1091  1105,
Issue 6,
December
2017
doi:10.3934/ipi.2017050 Abstract
References
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Ming Li  School of Mechanical Engineering, University of Shanghai for Science and Technology, 200093 Shanghai, China (email)
Ruming Zhang  Center for Industrial Mathematics, University of Bremen, 28359 Bremen, Germany (email)
1 
T. Arens, D. Gintides and A. Lechleiter, Direct and inverse medium scattering in a threedimensional homogeneous planar waveguide, SIAM J. Appl. Math., 71 (2011), 753772. 

2 
G. Bao, L. Cowsar and W. Masters, Mathematical Modeling in Optical Science, SIAM, Philadelphia, 2001. 

3 
L. Bourgeois and S. Fliss, On the identification of defects in a periodic waveguide from far field data, Inverse Problems, 30 (2014), 095004, 31pp. 

4 
L. Bourgeois and E. LunĂ©ville, The linear sampling method in a waveguide: A modal formulation, Inverse Problems, 24 (2008), 015018, 20pp. 

5 
L. Bourgeois and E. LunĂ©ville, On the use of sampling methods to identify cracks in acoustic waveguides, Inverse Problems, 28 (2012), 105011, 18pp. 

6 
G. Bruckner and J. Elschner, A twostep algorithm for the reconstruction of perfectly reflecting periodic profiles, Inverse Problems, 19 (2003), 315329. 

7 
G. Bruckner and J. Elschner, The numerical solution of an inverse periodic transmission problem, Math. Meth. Appl. Sci., 28 (2005), 757778. 

8 
C. Burkard and R. Potthast, A multisection approach for rough surface reconstruction via the KirschKress scheme, Inverse Problems, 26 (2010), 045007, 23pp. 

9 
D. Colton, R. Ewing and W. Rundell, Inverse Problems in Partial Differential Equation, SIAM, Phialdelphia, 1990. 

10 
M. Ehrhardt, H. Han and C. Zheng, Numerical simulation of waves in periodic structures, Commun. Comput. Phys., 5 (2009), 849870. 

11 
M. Ehrhardt, J. Sun and C. Zheng, Evaluation of scattering operators for semiinfinite periodic arrays, Commun. Math. Sci., 7 (2009), 347364. 

12 
J. Elschner and G. Hu, An optimization method in inverse elastic scattering for onedimensional grating profiles, Commun. Comput. Phys., 12 (2012), 14341460. 

13 
S. Fliss and P. Joly, Exact boundary conditions for timeharmonic wave propagation in locally perturbed periodic media, Appl. Numer. Math., 59 (2009), 21552178. 

14 
P. Joly, J. Li and S. Fliss, Exact boundary conditions for periodic waveguides containing a local perturbation, Commun. Comput. Phys., 1 (2006), 945973. 

15 
A. Kirsch and R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in Inverse Problems, Oberwolfach, 77 (1986), 93102. 

16 
A. Kirsch and R. Kress, A numerical method for an inverse scattering problem, in Inverse and Illposed Problems (ed. Sankt Wolfgang), Academic Press, Boston, 4 (1987), 279290. 

17 
A. Kirsch and R. Kress, An optimisition method in inverse acoustic scattering, in Boundary Elements IX, Stuttgart, 3 (1987), 318. 

18 
A. Kirsch, R. Kress, P. Monk and A. Zinn, Two methods for solving the inverse acoustic scattering problem, Inverse Problems, 4 (1988), 749770. 

19 
J. Li, G. Sun and B. Zhang, The KirschKress method for inverse scattering by infinite locally rough interfaces, Appl. Ana., 96 (2017), 85107. 

20 
J. Li, H. Liu and J. Zou, Locating multiple multiscale acoustic scatterers, Multiscale Model. Simul., 12 (2014), 927952. 

21 
J. Li, H. Liu and Q. Wang, Locating multiple multiscale electromagnetic scatterers by a single farfield measurement, SIAM J. Imaging Sciences, 6 (2013), 22852309. 

22 
J. Li, P. Li, H. Liu and X. Liu, Recovering multiscale buried anomalies in a twolayered medium, Inverse Problems, 31) (2015), 105006, 28pp. 

23 
P. Monk and V. Selgas, Sampling type methods for an inverse waveguide problem, Inverse Problems and Imaging, 6 (2012), 709747. 

24 
K. Sakoda, Optical Properties of Photonic Crystals, SpringerVerlag, Berlin, 2001. 

25 
J. Sun and C. Zheng, Numerical scattering analysis of TE plane waves by a metallic diffraction grating with local defects, J. Opt. Soc. Am. A., 26 (2009), 156162. 

26 
J. Sun and C. Zheng, Reconstruction of obstacles embedded in waveguides, Contemporary Mathematics, 586 (2013), 341350. 

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