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Detecting the localization of elastic inclusions and Lamé coefficients
1. | CEMAT-IST and Departamento de Matemática, Faculdade de Ciências e Tecnologia (NULisbon), Universidade Nova de Lisboa, Quinta da Torre, Caparica, Portugal |
References:
[1] |
C. J. S. Alves and H. Ammari, Boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium, SIAM Journal on Applied Mathematics, 62 (2001), 94-106.
doi: 10.1137/S0036139900369266. |
[2] |
C. J. S. Alves, M. J. Colaço, V. M. A. Leitão, N. F. M. Martins, H. R. B. Orlande and N. C. Roberty, Recovering the source term in a linear diffusion problem by the Method of Fundamental Solutions, Inverse Problems in Science and Engineering, 16 (2008), 1005-1021.
doi: 10.1080/17415970802083243. |
[3] |
C. J. S. Alves and N. F. M. Martins, Reconstruction of inclusions or cavities in potential problems using the MFS, in The Method of Fundamental Solutions-A Meshless Method (eds. C. S. Chen, A. Karageorghis and Y. S. Smyrlis), Dynamic Publishers Inc., 2008, 51-71. |
[4] |
C. J. S. Alves and N. F. M. Martins, The direct method of fundamental solutions and the inverse Kirsch-Kress method for the reconstruction of elastic inclusions or cavities, Journal of Integral Equations and Applications, 21 (2009), 153-178.
doi: 10.1216/JIE-2009-21-2-153. |
[5] |
C. J. S. Alves, N. F. M. Martins and N. C. Roberty, Full identification of acoustic sources with multiple frequencies and boundary measurements, Inverse Problems and Imaging, 3 (2009), 275-294.
doi: 10.3934/ipi.2009.3.275. |
[6] |
C. J. S. Alves and N. C. Roberty, On the identification of star shape sources from boundary measurements using a reciprocity functional, Inverse Problems in Science and Engineering, 17 (2009), 187-202.
doi: 10.1080/17415970802082799. |
[7] |
S. Andrieux and A. B. Abda, The reciprocity gap: A general concept for flaws identification, Mechanics Research Communication, 20 (1993), 415-420.
doi: 10.1016/0093-6413(93)90032-J. |
[8] |
G. Chen and J. Zhou, Boundary Element Methods, Computational Mathematics and Applications, Academic Press, London, 1992. |
[9] |
M. J. Colaço and C. J. S. Alves, A fast non-intrusive method for estimating spatial thermal contact conductante by means of the reciprocity functional approach and the method of fundamental solutions, International Journal of Heat and Mass Transfer, 60 (2013), {653-663}. |
[10] |
S. Cox and M. Gockenbach, Recovering planar Lamé moduli from a single traction experiment, Mathematics and Mechanics of Solids, 2 (1997), 297-306.
doi: 10.1177/108128659700200304. |
[11] |
A. El-Badia and T. Ha Duong, Some remarks on the problem of source identification from boundary measurements, Inverse Problems, 14 (1998), 883-891.
doi: 10.1088/0266-5611/14/4/008. |
[12] |
L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, 19, American Mathematical Society, 1998. |
[13] |
M. S. Gockenbach, B. Jadamba and A. A. Khan, Equation error approach for elliptic inverse problems with an application to the identification of Lamé parameters, Inverse Problems in Science and Engineering, 16 (2008), 349-367.
doi: 10.1080/17415970701602580. |
[14] |
B. Jadamba, A. A. Khan and F. Raciti, On the inverse problem of identifying Lamé coefficients in linear elasticity, Computers and Mathematics with Applications, 56 (2008), 431-443.
doi: 10.1016/j.camwa.2007.12.016. |
[15] |
Y. Liu, L. Z. Sun and G. Wang, Tomography based 3D anisotropic elastography using boundary measurements, IEEE Transactions on Medical Imaging, 24 (2005), 1323-1333. |
[16] |
L. Marin, L. L. Elliot, D. B. Ingham and D. Lesnic, Identification of material properties and cavities in two-dimensional linear elasticity, Computational Mechanics, 31 (2003), 293-300. |
[17] |
N. F. M. Martins and D. Soares, Localization of Immersed Obstacles from a Pair of Boundary Data, Proceedings of Jornadas do Mar, Escola Naval, Portugal (2012), (IN CDROM). |
[18] |
W. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, Cambridge, 2000. |
[19] |
G. Nakamura and G. Uhlmann, Identification of Lamé parameters by boundary measurements, American Journal of Mathematics, 115 (1993), 1161-1187.
doi: 10.2307/2375069. |
[20] |
N. Tlatli-Hariga, R. Bouhlila and A. B. Abda, Recovering data in groundwater: Boundary conditions and well's positions and fluxes, Computational Geosciences, 15 (2011), 637-645.
doi: 10.1007/s10596-011-9231-9. |
show all references
References:
[1] |
C. J. S. Alves and H. Ammari, Boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium, SIAM Journal on Applied Mathematics, 62 (2001), 94-106.
doi: 10.1137/S0036139900369266. |
[2] |
C. J. S. Alves, M. J. Colaço, V. M. A. Leitão, N. F. M. Martins, H. R. B. Orlande and N. C. Roberty, Recovering the source term in a linear diffusion problem by the Method of Fundamental Solutions, Inverse Problems in Science and Engineering, 16 (2008), 1005-1021.
doi: 10.1080/17415970802083243. |
[3] |
C. J. S. Alves and N. F. M. Martins, Reconstruction of inclusions or cavities in potential problems using the MFS, in The Method of Fundamental Solutions-A Meshless Method (eds. C. S. Chen, A. Karageorghis and Y. S. Smyrlis), Dynamic Publishers Inc., 2008, 51-71. |
[4] |
C. J. S. Alves and N. F. M. Martins, The direct method of fundamental solutions and the inverse Kirsch-Kress method for the reconstruction of elastic inclusions or cavities, Journal of Integral Equations and Applications, 21 (2009), 153-178.
doi: 10.1216/JIE-2009-21-2-153. |
[5] |
C. J. S. Alves, N. F. M. Martins and N. C. Roberty, Full identification of acoustic sources with multiple frequencies and boundary measurements, Inverse Problems and Imaging, 3 (2009), 275-294.
doi: 10.3934/ipi.2009.3.275. |
[6] |
C. J. S. Alves and N. C. Roberty, On the identification of star shape sources from boundary measurements using a reciprocity functional, Inverse Problems in Science and Engineering, 17 (2009), 187-202.
doi: 10.1080/17415970802082799. |
[7] |
S. Andrieux and A. B. Abda, The reciprocity gap: A general concept for flaws identification, Mechanics Research Communication, 20 (1993), 415-420.
doi: 10.1016/0093-6413(93)90032-J. |
[8] |
G. Chen and J. Zhou, Boundary Element Methods, Computational Mathematics and Applications, Academic Press, London, 1992. |
[9] |
M. J. Colaço and C. J. S. Alves, A fast non-intrusive method for estimating spatial thermal contact conductante by means of the reciprocity functional approach and the method of fundamental solutions, International Journal of Heat and Mass Transfer, 60 (2013), {653-663}. |
[10] |
S. Cox and M. Gockenbach, Recovering planar Lamé moduli from a single traction experiment, Mathematics and Mechanics of Solids, 2 (1997), 297-306.
doi: 10.1177/108128659700200304. |
[11] |
A. El-Badia and T. Ha Duong, Some remarks on the problem of source identification from boundary measurements, Inverse Problems, 14 (1998), 883-891.
doi: 10.1088/0266-5611/14/4/008. |
[12] |
L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, 19, American Mathematical Society, 1998. |
[13] |
M. S. Gockenbach, B. Jadamba and A. A. Khan, Equation error approach for elliptic inverse problems with an application to the identification of Lamé parameters, Inverse Problems in Science and Engineering, 16 (2008), 349-367.
doi: 10.1080/17415970701602580. |
[14] |
B. Jadamba, A. A. Khan and F. Raciti, On the inverse problem of identifying Lamé coefficients in linear elasticity, Computers and Mathematics with Applications, 56 (2008), 431-443.
doi: 10.1016/j.camwa.2007.12.016. |
[15] |
Y. Liu, L. Z. Sun and G. Wang, Tomography based 3D anisotropic elastography using boundary measurements, IEEE Transactions on Medical Imaging, 24 (2005), 1323-1333. |
[16] |
L. Marin, L. L. Elliot, D. B. Ingham and D. Lesnic, Identification of material properties and cavities in two-dimensional linear elasticity, Computational Mechanics, 31 (2003), 293-300. |
[17] |
N. F. M. Martins and D. Soares, Localization of Immersed Obstacles from a Pair of Boundary Data, Proceedings of Jornadas do Mar, Escola Naval, Portugal (2012), (IN CDROM). |
[18] |
W. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, Cambridge, 2000. |
[19] |
G. Nakamura and G. Uhlmann, Identification of Lamé parameters by boundary measurements, American Journal of Mathematics, 115 (1993), 1161-1187.
doi: 10.2307/2375069. |
[20] |
N. Tlatli-Hariga, R. Bouhlila and A. B. Abda, Recovering data in groundwater: Boundary conditions and well's positions and fluxes, Computational Geosciences, 15 (2011), 637-645.
doi: 10.1007/s10596-011-9231-9. |
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