[1] |
F. J. Fahy, P. Gardonio, Sound and Structural Vibration: Radiation, Transmission and Response, Academic Press, London, 2007. https://doi.org/10.1016/B978-0-12-373633-8.X5000-5 |
[2] |
M. Fatemi, J. F. Greenleaf, Ultrasound-Stimulated Vibro-Acoustic Spectrography, Science, 280 (1998), 82-85. https://doi.org/10.1126/science.280.5360.8 doi: 10.1126/science.280.5360.8 · doi:10.1126/science.280.5360.8 |
[3] |
H. Morand, R. Ohayon, Fluid Structure Interaction, Wiley, New York, 1995. https://doi.org/10.1007/3-540-34596-5 · Zbl 0834.73002 · doi:10.1007/3-540-34596-5 |
[4] |
M. Sanna, Numerical simulation of fluid-structure interaction between acoustic and elastic waves, Nihon Rinsho, 70 (2011), 685-696. https://doi.org/10.1051/aacus/2021014 doi: 10.1051/aacus/2021014 · doi:10.1051/aacus/2021014 |
[5] |
B. Desjardins, M. J. Esteban, C. Grandmont and P. Le Tallec, Weak solutions for a fluid-elastic structure interaction model, Revista Matemtica Complutense, 2 (2001), 523-538. https://doi.org/10.5209/rev-REMA.2001.v14.n2.17030 doi: 10.5209/rev-REMA.2001.v14.n2.17030 · Zbl 1007.35055 · doi:10.5209/rev-REMA.2001.v14.n2.17030 |
[6] |
G. Hsiao, R. E. Kleinman, G. F. Roach, Weak Solutions of Fluid-Solid Interaction Problems, Math. Nachr., 218 (2000), 139-163. https://doi.org/10.1002/1522-2616 doi: 10.1002/1522-2616 · Zbl 0963.35043 · doi:10.1002/1522-2616 |
[7] |
A. Bernardo, A. Mrquez, S. Meddahi, Analysis of an interaction problem between an electromagnetic field and an elastic body, Int. J. Num. Anal. Model., 7 (2010), 749-765. http://www.math.ualberta.ca/ijnam/Volume-7-2010/No-4-10/2010-04-10.pdf · Zbl 1193.78023 |
[8] |
G. N. Gatica, A. Mrquez, S. Meddahi, Analysis of the coupling of BEM, FEM, and mixed-FEM for a two-dimensional fluid-solid interaction problem, Appl. Num. Math., 59 (2009), 2735-2750. https://doi.org/10.1016/j.apnum.2008.12.025 doi: 10.1016/j.apnum.2008.12.025 · Zbl 1171.76027 · doi:10.1016/j.apnum.2008.12.025 |
[9] |
G. N. Gatica, A. Mrquez, S. Meddahi, Analysis of the Coupling of Lagrange and Arnold-Falk-Winther Finite Elements for a Fluid-Solid Interaction Problem in Three Dimensions, SIAM J. Numer. Anal., 50 (2012), 1648-1674. https://doi.org/10.1137/110836705 doi: 10.1137/110836705 · Zbl 1426.76262 · doi:10.1137/110836705 |
[10] |
X. Jiang, P. Li, An adaptive finite element PML method for the acoustic-elastic interaction in three dimensions, Commun. Comput. Phys., 22 (2017), 1486-1507. https://doi.org/10.4208/cicp.OA-2017-0047 doi: 10.4208/cicp.OA-2017-0047 · Zbl 1488.65627 · doi:10.4208/cicp.OA-2017-0047 |
[11] |
G. C. Everstine, F. M. Henderson, Coupled finite element/boundary element approach for fluid-structure interaction, J. Acoust. Soc. Amer., 87 (1990), 1938-1947. https://doi.org/10.1121/1.399320 doi: 10.1121/1.399320 · doi:10.1121/1.399320 |
[12] |
G. N. Gatica, A. Mrquez, S. Meddahi, Analysis of an augmented fully-mixed finite element method for a three-dimensional fluid-solid interaction problem, Int. J. Num. Anal. Model., 11 (2014), 624-656. http://www.math.ualberta.ca/ijnam/Volume-11-2014/No-3-14/2014-03-10.pdf · Zbl 1499.65660 |
[13] |
D. T. Wilton, Acoustic radiation and scattering from elastic structures, Int. J. Numer. Meth. Eng., 13 (1978), 123-138. https://doi.org/10.1002/nme.1620130109 doi: 10.1002/nme.1620130109 · Zbl 0384.76059 · doi:10.1002/nme.1620130109 |
[14] |
A. Boström, Scattering of stationary acoustic waves by an elastic obstacle immersed in a fluid, J. Acoust. Soc. Amer., 67 (1980), 390-398. https://doi.org/10.1121/1.383925 doi: 10.1121/1.383925 · Zbl 0454.76070 · doi:10.1121/1.383925 |
[15] |
A. Boström, Scattering of acoustic waves by a layered elastic obstacle in a fluid-An improved nullfield approach, J. Acoust. Soc. Amer., 76 (1984), 588-593. https://doi.org/10.1121/1.391154 doi: 10.1121/1.391154 · Zbl 0564.73033 · doi:10.1121/1.391154 |
[16] |
B. Yildirim, S. Lin, S. Mathur, J.Y. Murthy, A parallel implementation of fluid-solid interaction solver using an immersed boundary method, Computers Fluids, 86 (2013), 251-274. · Zbl 1290.76007 |
[17] |
Q. Zhang, R. D. Guy, B. Philip, A projection preconditioner for solving the implicit immersed boundary equations, Numer. Math. Theor. Meth. Appl., 7 (2014), 473-498. https://doi.org/10.1017/S100489790000129X doi: 10.1017/S100489790000129X · Zbl 1324.76043 · doi:10.1017/S100489790000129X |
[18] |
Y. He, J. Shen, Unconditionally stable pressure-correction schemes for a linear fluid-structure interaction problem, Numer. Math. Theor. Meth. Appl., 7 (2014), 537-554. https://doi.org/10.1017/S1004897900001331 doi: 10.1017/S1004897900001331 · Zbl 1324.76040 · doi:10.1017/S1004897900001331 |
[19] |
J. Li, H. Liu, Y. Wang, Recovering an electromagnetic obstacle by a few phaseless backscattering measurements, Inverse Problems, 33 (2017), 035011. https://doi.org/10.1088/1361-6420/aa5bf3 doi: 10.1088/1361-6420/aa5bf3 · Zbl 1432.78008 · doi:10.1088/1361-6420/aa5bf3 |
[20] |
H. Liu, M. Petrini, L. Rondi, J. Xiao, Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements, J. Differential Equations, 262 (2017), 1631-1670. https://doi.org/10.1016/j.jde.2016.10.021 doi: 10.1016/j.jde.2016.10.021 · Zbl 1352.74148 · doi:10.1016/j.jde.2016.10.021 |
[21] |
H. Liu, L. Rondi, J. Xiao, Mosco convergence for spaces, higher integrability for Maxwell’s equations, and stability in direct and inverse EM scattering problems, J. Eur. Math. Soc., 21 (2019), 2945-2993. https://doi.org/10.4171/JEMS/895 doi: 10.4171/JEMS/895 · Zbl 1502.78020 · doi:10.4171/JEMS/895 |
[22] |
J. Li, P. Li, H. Liu, X. Liu, Recovering multiscale buried anomalies in a two-layered medium, Inverse Problems, 31 (2015), 105006. https://doi.org/10.1088/0266-5611/31/10/105006 doi: 10.1088/0266-5611/31/10/105006 · Zbl 1330.78012 · doi:10.1088/0266-5611/31/10/105006 |
[23] |
M. Abdelwahed, L. C. Berselli, N. Chorfi, On the uniqueness for weak solutions of steady double-phase fluids, Adv. Nonlinear Anal., 11 (2022), 454-468. https://doi.org/10.1515/anona-2020-0196 doi: 10.1515/anona-2020-0196 · Zbl 1484.76003 · doi:10.1515/anona-2020-0196 |
[24] |
R. Farwig, R. Kanamaru, Optimality of Serrin type extension criteria to the Navier-Stokes equations, Adv. Nonlinear Anal., 10 (2021), 1071-1085. https://doi.org/10.1515/anona-2020-0130 doi: 10.1515/anona-2020-0130 · Zbl 1473.35400 · doi:10.1515/anona-2020-0130 |
[25] |
M. Jenaliyev, M. Ramazanov, M. Yergaliyev, On the numerical solution of one inverse problem for a linearized two-dimensional system of Navier-Stokes equations, Opuscula Math., 42 (2022), 709-725. https://doi.org/10.7494/OpMath.2022.42.5.709 doi: 10.7494/OpMath.2022.42.5.709 · Zbl 1498.35390 · doi:10.7494/OpMath.2022.42.5.709 |
[26] |
Y. Sun, X. Lu, B. Chen, The method of fundamental solutions for the high frequency acoustic-elastic problem and its relationship to a pure acoustic problem, Eng. Anal. Bound. Elem., 156 (2023), 299-310. https://doi.org/10.1016/j.enganabound.2023.08.010 doi: 10.1016/j.enganabound.2023.08.010 · Zbl 1539.74505 · doi:10.1016/j.enganabound.2023.08.010 |
[27] |
Y. Wang, W. Wu, Initial boundary value problems for the three-dimensional compressible elastic Navier-Stokes-Poisson equations, Adv. Nonlinear Anal., 10 (2021), 1356-1383. https://doi.org/10.1515/anona-2020-0184 doi: 10.1515/anona-2020-0184 · Zbl 1472.76003 · doi:10.1515/anona-2020-0184 |
[28] |
F. Bu, J. Lin, F. Reitich, A fast and high-order method for the three-dimensional elastic wave scattering problem, J. Comput. Phy., 258 (2014), 856-870. https://doi.org/10.1016/j.jcp.2013.11.009 doi: 10.1016/j.jcp.2013.11.009 · Zbl 1349.74348 · doi:10.1016/j.jcp.2013.11.009 |
[29] |
M. Costabel, E. Stephan, A direct boundary integral equation method for transmission problems, J. Math. Anal. Appl., 106 (1985), 205-220. https://doi.org/10.1016/0022-247X(85)90118-0 doi: 10.1016/0022-247X(85)90118-0 · Zbl 0597.35021 · doi:10.1016/0022-247X(85)90118-0 |
[30] |
G. Hsiao, L. Xu, A system of boundary integral equations for the transmission problem in acoustics, J. Comput. Appl. Math., 61 (2011), 1017-1029. https://doi.org/10.1016/j.apnum.2011.05.003 doi: 10.1016/j.apnum.2011.05.003 · Zbl 1387.76072 · doi:10.1016/j.apnum.2011.05.003 |
[31] |
R. Kleinman, P. Martin, On single integral equations for the transmission problem of acoustics, SIAM J. Appl. Math., 48 (1998), 307-325. https://doi.org/10.1137/0148016 doi: 10.1137/0148016 · Zbl 0663.76095 · doi:10.1137/0148016 |
[32] |
Y. Sun, Indirect boundary integral equation method for the Cauchy problem of the Laplace equation, J. Sci. Comput., 71 (2017), 469-498. https://doi.org/10.1007/s10915-016-0308-4 doi: 10.1007/s10915-016-0308-4 · Zbl 1387.31002 · doi:10.1007/s10915-016-0308-4 |
[33] |
C. Luke, P. Martin, Fluid-solid interaction: acoustic scattering by a smooth elastic obstacle, SIAM J. Appl. Math., 55 (1995), 904-923. https://doi.org/10.1137/S0036139993259027 doi: 10.1137/S0036139993259027 · Zbl 0832.73045 · doi:10.1137/S0036139993259027 |
[34] |
E. Atkinson, The numerical solution of integral equations of the second kind, Cambridge University Press, Cambridge, 1997. https://doi.org/10.1017/CBO9780511626340 · Zbl 0899.65077 |
[35] |
B. Alpert, Hybrid Gauss-trapezoidal quadrature rules, SIAM J. Sci. Comput., 20 (1999), 1551-1584. https://doi.org/10.1137/S106482759732514 doi: 10.1137/S106482759732514 · Zbl 0933.41019 · doi:10.1137/S106482759732514 |
[36] |
R. Kress, On the numerical solution of a hypersingular integral equation in scattering theory, J. Comput. Appl. Math., 61 (1995), 345-360. https://doi.org/10.1016/0377-0427(94)00073-7 doi: 10.1016/0377-0427(94)00073-7 · Zbl 0839.65119 · doi:10.1016/0377-0427(94)00073-7 |
[37] |
R. Kress, I. H. Sloan, On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation, Numer. Math., 66 (1993), 199-214. https://doi.org/10.1007/BF01385694 doi: 10.1007/BF01385694 · Zbl 0791.65089 · doi:10.1007/BF01385694 |
[38] |
R. Kress, A collocation method for a hypersingular boundary integral equation via trigonometric differentiation, J. Integral Equations Appl., 26 (2014), 197-213. https://doi.org/10.1216/JIE-2014-26-2-197 doi: 10.1216/JIE-2014-26-2-197 · Zbl 1310.65169 · doi:10.1216/JIE-2014-26-2-197 |
[39] |
D. S. Jones, Low frequency scattering by a body in lubricated contact, Quarterly Journal of Mechanics and Applied Mathematics, 36 (1983), 111-138. https://doi.org/10.1093/qjmam/36.1.111 doi: 10.1093/qjmam/36.1.111 · Zbl 0552.73023 · doi:10.1093/qjmam/36.1.111 |
[40] |
D. Natroshvili, G. Sadunishvili, I. Sigua, Some remarks concerning Jones eigenfrequencies and Jones modes, Georgian Mathematical Journal, 12 (2005), 337-348. https://doi.org/10.1515/GMJ.2005.337 doi: 10.1515/GMJ.2005.337 · Zbl 1138.74327 · doi:10.1515/GMJ.2005.337 |
[41] |
T. Yin, G. C. Hsiao, L. Xu, Boundary integral equation methods for the two dimensional fluid-solid interaction problem, SIAM J. Numer. Anal., 55 (2017), 2361-2393. https://doi.org/10.1137/16M107567 doi: 10.1137/16M107567 · Zbl 1386.35056 · doi:10.1137/16M107567 |
[42] |
H. Dong, J. Lai, P. Li, Inverse obstacle scattering for elastic waves with phased or phaseless far-field data, SIAM J. Imaging Sci., 12 (2019), 809-838. https://doi.org/10.1137/18M122726 doi: 10.1137/18M122726 · Zbl 1524.78044 · doi:10.1137/18M122726 |
[43] |
H. Dong, J. Lai, P. Li, An inverse acoustic-elsatic interaction problem with phased or phaseless far-field data, Inverse Probl., 36 (2020), 035014. https://doi.org/10.1088/1361-6420/ab693e doi: 10.1088/1361-6420/ab693e · Zbl 1437.35702 · doi:10.1088/1361-6420/ab693e |
[44] |
R. Kress, Linear integral equations, 3 ed., Spronger, New York, 2014. https://doi.org/10.1007/978-1-4614-9593-2 · Zbl 1328.45001 · doi:10.1007/978-1-4614-9593-2 |
[45] |
J. Lai, P. Li, A framework for simulation of multiple elastic scattering in two dimensions, SIAM J. Sci. Comput., 41 (2019), 3276-3299. https://doi.org/10.1137/18M123281 doi: 10.1137/18M123281 · Zbl 1439.35358 · doi:10.1137/18M123281 |
[46] |
D. Colton, R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3 edn (New York: Springer), 2013. https://link.springer.com/book/10.1007/978-1-4614-4942-3 · Zbl 1266.35121 |
[47] |
H. Dong, J. Lai, P. Li, A highly accurate boundary integral method for the elastic obstaclescattering problem, Math. Comput., 90 (2021), 2785-2814. https://doi.org/10.1090/mcom/3660 doi: 10.1090/mcom/3660 · Zbl 1479.65035 · doi:10.1090/mcom/3660 |
[48] |
A. Kirsch, An introduction to the mathematical theory of inverse problems, New York, 2011. https://doi.org/10.1007/978-1-4419-8474-6 · Zbl 1213.35004 · doi:10.1007/978-1-4419-8474-6 |
[49] |
Z. Fu, Q. Xi, Y. Gu, J. Li, W. Qu, L. Sun, et al. Singular boundary method: A review and computer implementation aspects, Eng. Anal. Bound. Elem., 147 (2023), 231-266. https://doi.org/10.1016/j.enganabound.2022.12.004 doi: 10.1016/j.enganabound.2022.12.004 · Zbl 1521.74318 · doi:10.1016/j.enganabound.2022.12.004 |
[50] |
Z. Fu, Q. Xi, Y. Li, H. Huang, T. Rabczuket, Hybrid FEM-SBM solver for structural vibration induced underwater acoustic radiation in shallow marine environment, Comput. Meth. Appl. Mech. Eng., 369 (2020), 113236. https://doi.org/10.1016/j.cma.2020.113236 doi: 10.1016/j.cma.2020.113236 · Zbl 1506.74137 · doi:10.1016/j.cma.2020.113236 |
[51] |
Z. Fu, W. Chen, P. H. Wen, C. Z. Zhang, Singular boundary method for wave propagation analysis in periodic structures, J. Sound Vib., 425 (2018), 170-188. https://doi.org/10.1016/j.jsv.2018.04.005 doi: 10.1016/j.jsv.2018.04.005 · doi:10.1016/j.jsv.2018.04.005 |