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. 
@article{TM_2016_295_a9,
     author = {D. Yu. Knyaz'kov and A. V. Romanova and A. S. Shamaev},
     title = {A local perturbation method for the approximate calculation of the acoustic wave diffraction with impedance interface conditions},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {184--194},
     publisher = {mathdoc},
     volume = {295},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2016_295_a9/}
}
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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/