Geodesic
Finite difference method in the problem of diffraction of a plane acoustic wave in a half-plane with a cut
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 12, pp. 2214-2231 
A. O. Rodnikov; B. A. Samokish. Finite difference method in the problem of diffraction of a plane acoustic wave in a half-plane with a cut. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 12, pp. 2214-2231. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_12_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the numerical solution of the diffraction problem for an acoustic plane wave in a half-plane with a cut, boundary conditions that are equivalent to the radiation conditions at infinity are set in a neighborhood of the points of the cut. Joining the physical boundary conditions on the cut, a closing set of equations of order $4N$, where $N$ is the number of grid points on the cut, is obtained. The so-called Green's grid function for the half-plane is used, which makes it possible to pass from one grid layer to another one for the solution satisfying certain conditions at infinity.

[1] Samokish B. A., “Primenenie metoda Fure dlya resheniya raznostnykh uravnenii”, Metody vychislenii, Vyp. 4, M., 1967, 97–101

[2] Voronkova A. I., “Reshenie pervoi kraevoi zadachi dlya bigarmonicheskogo uravneniya v polupolose s pomoschyu setochnoi funktsii Grina”, Zh. vychisl. matem. i matem. fiz., 11:3 (1971), 667–676 | MR | Zbl

[3] Nikiforova E. V., “Raschet gravitatsionnykh plotin sovmestno s uprugim osnovaniem metodom setok na ETsVM”, Izv. VNIIG, 86 (1968), 199–212

[4] Ryabenkii B. C., Metod raznostnykh potentsialov i ego prilozheniya, Izd. 2-e dop. i ispr., Fizmatlit, M., 2002

[5] Lyalinov M. A., “O zadache difraktsii v oblasti s tonkim pokrytiem granitsy”, Zap. nauchn. seminarov POMI, 239, 157–171 | MR

[6] Ryabenkii B. C., “Metod vnutrennikh granichnykh uslovii v teorii raznostnykh skhem”, Uspekhi matem. nauk, 26:3 (1971), 105–160 | MR

[7] Smirnov V. I., Kurs vysshei matematiki, T. 4. Ch. 2, Nauka, M., 1967