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Inverse Problems and Imaging (IPI)
 

Near-field imaging of sound-soft obstacles in periodic waveguides
Pages: 1091 - 1105, Issue 6, December 2017

doi:10.3934/ipi.2017050      Abstract        References        Full text (733.7K)           Related Articles

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 three-dimensional homogeneous planar waveguide, SIAM J. Appl. Math., 71 (2011), 753-772.       
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 two-step algorithm for the reconstruction of perfectly reflecting periodic profiles, Inverse Problems, 19 (2003), 315-329.       
7 G. Bruckner and J. Elschner, The numerical solution of an inverse periodic transmission problem, Math. Meth. Appl. Sci., 28 (2005), 757-778.       
8 C. Burkard and R. Potthast, A multi-section approach for rough surface reconstruction via the Kirsch-Kress 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), 849-870.       
11 M. Ehrhardt, J. Sun and C. Zheng, Evaluation of scattering operators for semi-infinite periodic arrays, Commun. Math. Sci., 7 (2009), 347-364.       
12 J. Elschner and G. Hu, An optimization method in inverse elastic scattering for one-dimensional grating profiles, Commun. Comput. Phys., 12 (2012), 1434-1460.       
13 S. Fliss and P. Joly, Exact boundary conditions for time-harmonic wave propagation in locally perturbed periodic media, Appl. Numer. Math., 59 (2009), 2155-2178.       
14 P. Joly, J. Li and S. Fliss, Exact boundary conditions for periodic waveguides containing a local perturbation, Commun. Comput. Phys., 1 (2006), 945-973.
15 A. Kirsch and R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in Inverse Problems, Oberwolfach, 77 (1986), 93-102.       
16 A. Kirsch and R. Kress, A numerical method for an inverse scattering problem, in Inverse and Ill-posed Problems (ed. Sankt Wolfgang), Academic Press, Boston, 4 (1987), 279-290.       
17 A. Kirsch and R. Kress, An optimisition method in inverse acoustic scattering, in Boundary Elements IX, Stuttgart, 3 (1987), 3-18.       
18 A. Kirsch, R. Kress, P. Monk and A. Zinn, Two methods for solving the inverse acoustic scattering problem, Inverse Problems, 4 (1988), 749-770.       
19 J. Li, G. Sun and B. Zhang, The Kirsch-Kress method for inverse scattering by infinite locally rough interfaces, Appl. Ana., 96 (2017), 85-107.       
20 J. Li, H. Liu and J. Zou, Locating multiple multiscale acoustic scatterers, Multiscale Model. Simul., 12 (2014), 927-952.       
21 J. Li, H. Liu and Q. Wang, Locating multiple multiscale electromagnetic scatterers by a single far-field measurement, SIAM J. Imaging Sciences, 6 (2013), 2285-2309.       
22 J. Li, P. Li, H. Liu and X. Liu, Recovering multiscale buried anomalies in a two-layered 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), 709-747.       
24 K. Sakoda, Optical Properties of Photonic Crystals, Springer-Verlag, 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), 156-162.       
26 J. Sun and C. Zheng, Reconstruction of obstacles embedded in waveguides, Contemporary Mathematics, 586 (2013), 341-350.       

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