Geodesic
A local perturbation method for the approximate calculation of the acoustic wave diffraction with impedance interface conditions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 295 (2016), pp. 184-194.

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The problem of incidence of an acoustic wave on the interface between media with impedance interface conditions is considered. An approximate method is proposed for calculating the result of diffraction under such conditions. The method is implemented as a computer program, and the result is compared with the analytical solution for the impedance conditions and with the calculations by a program for the contact boundary conditions. Good accuracy of the method and high computation speed are demonstrated, which allow one to apply the proposed approximate method to solving both direct and inverse problems of acoustics. 
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D. Yu. Knyaz'kov; A. V. Romanova; A. S. Shamaev. A local perturbation method for the approximate calculation of the acoustic wave diffraction with impedance interface conditions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 295 (2016), pp. 184-194. http://geodesic.mathdoc.fr/item/TM_2016_295_a9/

[1] Brekhovskikh L. M., Godin O. A., Akustika neodnorodnykh sred, v. 1, Nauka, M., 2007

[2] Embleton T. F. W., Piercy J. E., Daigle G. A., “Effective flow resistivity of ground surfaces determined by acoustical measurements”, J. Acoust. Soc. Amer., 74:4 (1983), 1239–1244 | DOI

[3] Isers A. B., Puzenko A. A., Fuks I. M., “Metod lokalnykh vozmuschenii resheniya zadach difraktsii voln na nerovnoi poverkhnosti”, DAN USSR. Ser. A, 1989, no. 9, 64–68

[4] Skuchik E., Osnovy akustiki, v. 1, Mir, M., 1976

[5] Nesterov V. S., “Vyazko-inertsionnaya dispersiya i zatukhanie zvuka v suspenzii vysokoi kontsentratsii”, Akust. zhurn., 5:3 (1959), 337–344 | MR

[6] Akulenko L. D., Nesterov S. V., “Inertsionnye i dissipativnye svoistva poristoi sredy, zapolnennoi vyazkoi zhidkostyu”, Izv. RAN. Mekhanika tverdogo tela, 2005, no. 1, 109–119

[7] Badyukov V. F., “Teoremy edinstvennosti dlya zadachi rasseyaniya na periodicheskoi poverkhnosti”, Vestn. LGU. Ser. mat., mekh., astron., 1977, no. 19, 88–92 | Zbl

[8] Badyukov V. F., “Teoremy suschestvovaniya dlya zadachi rasseyaniya na periodicheskoi poverkhnosti”, Vestn. LGU. Ser. mat., mekh., astron., 1978, no. 1, 81–88 | Zbl

[9] Galishnikova T. N., Ilinskii A. S., Chislennye metody v zadachakh difraktsii, Izd-vo MGU, M., 1987 | MR

[10] Ilinskii A. S., Slepyan G. Ya., Kolebaniya i volny v elektrodinamicheskikh sistemakh s poteryami, Izd-vo MGU, M., 1983 | MR

[11] Mikheev A. G., Tkachenko T. L., “Asimptoticheskie metody v zadache difraktsii na volnistoi poverkhnosti”, Vestn. Mosk. un-ta. Vychisl. matematika i kibernetika, 1993, no. 1, 3–9 | MR

[12] Grünberg G. A., “Theory of the coastal refraction of electromagnetic waves”, Acad. Sci. USSR J. Phys., 6:5 (1942), 185–209 | MR

[13] Brekhovskikh L., “Predely primenimosti nekotorykh priblizhennykh metodov, upotreblyaemykh v arkhitekturnoi akustike: Po povodu stati Morza i Bolta ‘Zvukovye volny v pomescheniyakh’ ”, UFN, 32:4 (1947), 464–479 | DOI

[14] Leontovich M. A., “O priblizhennykh granichnykh usloviyakh dlya elektromagnitnogo polya na poverkhnosti khorosho provodyaschikh tel”, Issledovaniya po rasprostraneniyu radiovoln, Sb. vtoroi, ed. B. A. Vvedenskii, Izd-vo AN SSSR, M.–L., 1948, 5–12

[15] Bass F. G., Fuks I. M., Rasseyanie voln na statisticheski nerovnoi poverkhnosti, Nauka, M., 1972 | MR

[16] Chernik V. V., “Primenenie metodov dekompozitsii i integralnykh preobrazovanii dlya resheniya zadachi prokhozhdeniya ploskoi volny cherez neodnorodnuyu sredu”, Tr. 57-i nauch. konf. MFTI. Aerofizika i kosmicheskie issledovaniya, MFTI, M., 2014, 23–24

[17] Ilinskii A. S., “Metod issledovaniya zadach difraktsii voln na periodicheskoi strukture”, ZhVMiMF, 14:4 (1974), 1063–1067 | MR

[18] http://ipmnet.ru/~knyaz/diffraction.html