-
Previous Article
The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain
- IPI Home
- This Issue
-
Next Article
Common midpoint versus common offset acquisition geometry in seismic imaging
Factorization method in inverse interaction problems with bi-periodic interfaces between acoustic and elastic waves
1. | Weierstrass Institute, Mohrenstr. 39, 10117 Berlin |
2. | Department of Mathematics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe |
3. | College of Mathematics and Statistics, Chongqing University, China |
References:
[1] |
T. Arens and N. Grinberg, A complete factorization method for scattering by periodic surface, Computing, 75 (2005), 111-132.
doi: 10.1007/s00607-004-0092-0. |
[2] |
T. Arens and A. Kirsch, The factorization method in inverse scattering from periodic structures, Inverse Problems, 19 (2003), 1195-1211.
doi: 10.1088/0266-5611/19/5/311. |
[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.
doi: 10.1002/mma.1670170502. |
[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.
doi: 10.1063/1.331829. |
[6] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Berlin, Springer, 1998.
doi: 10.1007/978-3-662-03537-5. |
[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.
doi: 10.1016/j.ultras.2005.03.008. |
[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.
doi: 10.1002/mma.1305. |
[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.
doi: 10.1142/S0218202511500199. |
[11] |
J. Elschner, G. C. Hsiao and A. Rathsfeld, An inverse problem for fluid-solid interaction, Inverse Problems and Imaging, 2 (2008), 83-119.
doi: 10.3934/ipi.2008.2.83. |
[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.
doi: 10.1137/080736922. |
[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.
doi: 10.1002/(SICI)1099-1476(19980925)21:14<1297::AID-MMA997>3.0.CO;2-C. |
[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.
doi: 10.1088/0266-5611/13/2/010. |
[17] |
G. C. Hsiao, R. E. Kleinman and G. F. Roach, Weak solution of fluid-solid interaction problem, Math. Nachr., 218 (2000), 139-163.
doi: 10.1002/1522-2616(200010)218:1<139::AID-MANA139>3.0.CO;2-S. |
[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.
doi: 10.1088/0266-5611/29/11/115005. |
[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.
doi: 10.1088/0266-5611/30/9/095005. |
[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.
doi: 10.1002/num.21980. |
[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.
doi: 10.1088/0266-5611/14/6/009. |
[23] |
A. Kirsch, Diffraction by periodic structures, in Proc. Lapland Conf. Inverse Problems, (eds. L. Päivärinta et al), Berlin, Springer, 422 (1993), 87-102.
doi: 10.1007/3-540-57195-7_11. |
[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.
doi: 10.3934/ipi.2012.6.681. |
[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.
doi: 10.1137/120903968. |
[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.
doi: 10.1137/S0036139993259027. |
[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.
doi: 10.3934/ipi.2009.3.173. |
[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.
doi: 10.3934/ipi.2011.5.465. |
show all references
References:
[1] |
T. Arens and N. Grinberg, A complete factorization method for scattering by periodic surface, Computing, 75 (2005), 111-132.
doi: 10.1007/s00607-004-0092-0. |
[2] |
T. Arens and A. Kirsch, The factorization method in inverse scattering from periodic structures, Inverse Problems, 19 (2003), 1195-1211.
doi: 10.1088/0266-5611/19/5/311. |
[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.
doi: 10.1002/mma.1670170502. |
[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.
doi: 10.1063/1.331829. |
[6] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Berlin, Springer, 1998.
doi: 10.1007/978-3-662-03537-5. |
[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.
doi: 10.1016/j.ultras.2005.03.008. |
[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.
doi: 10.1002/mma.1305. |
[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.
doi: 10.1142/S0218202511500199. |
[11] |
J. Elschner, G. C. Hsiao and A. Rathsfeld, An inverse problem for fluid-solid interaction, Inverse Problems and Imaging, 2 (2008), 83-119.
doi: 10.3934/ipi.2008.2.83. |
[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.
doi: 10.1137/080736922. |
[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.
doi: 10.1002/(SICI)1099-1476(19980925)21:14<1297::AID-MMA997>3.0.CO;2-C. |
[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.
doi: 10.1088/0266-5611/13/2/010. |
[17] |
G. C. Hsiao, R. E. Kleinman and G. F. Roach, Weak solution of fluid-solid interaction problem, Math. Nachr., 218 (2000), 139-163.
doi: 10.1002/1522-2616(200010)218:1<139::AID-MANA139>3.0.CO;2-S. |
[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.
doi: 10.1088/0266-5611/29/11/115005. |
[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.
doi: 10.1088/0266-5611/30/9/095005. |
[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.
doi: 10.1002/num.21980. |
[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.
doi: 10.1088/0266-5611/14/6/009. |
[23] |
A. Kirsch, Diffraction by periodic structures, in Proc. Lapland Conf. Inverse Problems, (eds. L. Päivärinta et al), Berlin, Springer, 422 (1993), 87-102.
doi: 10.1007/3-540-57195-7_11. |
[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.
doi: 10.3934/ipi.2012.6.681. |
[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.
doi: 10.1137/120903968. |
[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.
doi: 10.1137/S0036139993259027. |
[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.
doi: 10.3934/ipi.2009.3.173. |
[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.
doi: 10.3934/ipi.2011.5.465. |
[1] |
Andreas Kirsch, Albert Ruiz. The Factorization Method for an inverse fluid-solid interaction scattering problem. Inverse Problems and Imaging, 2012, 6 (4) : 681-695. doi: 10.3934/ipi.2012.6.681 |
[2] |
Johannes Elschner, George C. Hsiao, Andreas Rathsfeld. An inverse problem for fluid-solid interaction. Inverse Problems and Imaging, 2008, 2 (1) : 83-120. doi: 10.3934/ipi.2008.2.83 |
[3] |
Beatrice Bugert, Gunther Schmidt. Analytical investigation of an integral equation method for electromagnetic scattering by biperiodic structures. Discrete and Continuous Dynamical Systems - S, 2015, 8 (3) : 435-473. doi: 10.3934/dcdss.2015.8.435 |
[4] |
Francesca Bucci, Irena Lasiecka. Regularity of boundary traces for a fluid-solid interaction model. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 505-521. doi: 10.3934/dcdss.2011.4.505 |
[5] |
Michael V. Klibanov. A phaseless inverse scattering problem for the 3-D Helmholtz equation. Inverse Problems and Imaging, 2017, 11 (2) : 263-276. doi: 10.3934/ipi.2017013 |
[6] |
Peter Monk, Virginia Selgas. An inverse fluid--solid interaction problem. Inverse Problems and Imaging, 2009, 3 (2) : 173-198. doi: 10.3934/ipi.2009.3.173 |
[7] |
Qinghua Wu, Guozheng Yan. The factorization method for a partially coated cavity in inverse scattering. Inverse Problems and Imaging, 2016, 10 (1) : 263-279. doi: 10.3934/ipi.2016.10.263 |
[8] |
S. L. Ma'u, P. Ramankutty. An averaging method for the Helmholtz equation. Conference Publications, 2003, 2003 (Special) : 604-609. doi: 10.3934/proc.2003.2003.604 |
[9] |
David Bourne, Howard Elman, John E. Osborn. A Non-Self-Adjoint Quadratic Eigenvalue Problem Describing a Fluid-Solid Interaction Part II: Analysis of Convergence. Communications on Pure and Applied Analysis, 2009, 8 (1) : 143-160. doi: 10.3934/cpaa.2009.8.143 |
[10] |
Stuart S. Antman, David Bourne. A Non-Self-Adjoint Quadratic Eigenvalue Problem Describing a Fluid-Solid Interaction Part I: Formulation, Analysis, and Computations. Communications on Pure and Applied Analysis, 2009, 8 (1) : 123-142. doi: 10.3934/cpaa.2009.8.123 |
[11] |
Peter Monk, Virginia Selgas. Near field sampling type methods for the inverse fluid--solid interaction problem. Inverse Problems and Imaging, 2011, 5 (2) : 465-483. doi: 10.3934/ipi.2011.5.465 |
[12] |
Jun Guo, Qinghua Wu, Guozheng Yan. The factorization method for cracks in elastic scattering. Inverse Problems and Imaging, 2018, 12 (2) : 349-371. doi: 10.3934/ipi.2018016 |
[13] |
Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system.. Evolution Equations and Control Theory, 2014, 3 (1) : 83-118. doi: 10.3934/eect.2014.3.83 |
[14] |
Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part I: The linearized system.. Evolution Equations and Control Theory, 2014, 3 (1) : 59-82. doi: 10.3934/eect.2014.3.59 |
[15] |
Guanqiu Ma, Guanghui Hu. Factorization method for inverse time-harmonic elastic scattering with a single plane wave. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022050 |
[16] |
Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems and Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271 |
[17] |
Jianliang Li, Jiaqing Yang, Bo Zhang. A linear sampling method for inverse acoustic scattering by a locally rough interface. Inverse Problems and Imaging, 2021, 15 (5) : 1247-1267. doi: 10.3934/ipi.2021036 |
[18] |
Stéphane Brull, Pierre Charrier, Luc Mieussens. Gas-surface interaction and boundary conditions for the Boltzmann equation. Kinetic and Related Models, 2014, 7 (2) : 219-251. doi: 10.3934/krm.2014.7.219 |
[19] |
Lorena Bociu, Jean-Paul Zolésio. Sensitivity analysis for a free boundary fluid-elasticity interaction. Evolution Equations and Control Theory, 2013, 2 (1) : 55-79. doi: 10.3934/eect.2013.2.55 |
[20] |
Lorena Bociu, Jean-Paul Zolésio. Existence for the linearization of a steady state fluid/nonlinear elasticity interaction. Conference Publications, 2011, 2011 (Special) : 184-197. doi: 10.3934/proc.2011.2011.184 |
2020 Impact Factor: 1.639
Tools
Metrics
Other articles
by authors
[Back to Top]