Geodesic
A method for approximate computation of the scattering matrix in acoustic diffraction gratings
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 52, Tome 516 (2022), pp. 238-252 
B. A. Plamenevsky; A. S. Poretsky; O. V. Sarafanov. A method for approximate computation of the scattering matrix in acoustic diffraction gratings. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 52, Tome 516 (2022), pp. 238-252. http://geodesic.mathdoc.fr/item/ZNSL_2022_516_a8/
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     title = {A method for approximate computation of the scattering matrix in acoustic diffraction gratings},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A two-dimensional reflection acoustic grating is considered. We formulate and justify a method for approximate computation of the scattering matrix describing the scattering of plane waves on the periodic boundary of this grating. To this purpose, the problem in the grating is reduced to a problem in an auxiliary waveguide. The known method for computing waveguide scattering matrices is expanded to the obtained waveguide. The suggested method is not influenced by surface waves in the grating.

[1] V. Grikurov, E. Heikkola, P. Neittaanmäki, B. Plamenevskii, “On computation of scattering matrices and on surface waves for diffraction gratings”, Numerische Mathematik, 94:2 (2003), 269–288 | DOI | MR

[2] B. A. Plamenevskii, O. V. Sarafanov, “O metode vychisleniya volnovodnykh matrits rasseyaniya v prisutstvii tochechnogo spektra”, Funkts. analiz prilozh., 48:1 (2014), 61–72 | MR

[3] P. Neittaanmyaki, B. A. Plamenevskii, O. V. Sarafanov, “Izluchenie i rasseyanie v oblastyakh s periodicheskimi volnovodami pri medlennoi stabilizatsii kharakteristik sredy”, Probl. matem. analiza, 64 (2012), 93–117

[4] B. A. Plamenevskii, O. V. Sarafanov, “O metode vychisleniya matrits rasseyaniya dlya volnovodov”, Algebra analiz, 23:1 (2011), 200–231

[5] L. Baskin, P. Neittaanmäki, B. Plamenevskii, O. Sarafanov, Resonant Tunneling: Quantum Waveguides of Variable Cross-Sections, Asymptotics, Numerics, and Applications, Lecture Notes on Numerical Methods in Engineering and Sciences, Springer, 2015 | DOI | MR

[6] B. A. Plamenevskii, A. S. Poretskii, O. V. Sarafanov, “O vychislenii volnovodnoi matritsy rasseyaniya dlya sistemy Maksvella”, Funkts. analiz prilozh., 49:1 (2015), 93–96

[7] B. A. Plamenevskii, A. S. Poretskii, O. V. Sarafanov, “Metod priblizhennogo vychisleniya volnovodnykh matrits rasseyaniya”, Uspekhi matem. nauk, 75:3 (2020), 123–182 | MR

[8] B. A. Plamenevskii, A. S. Poretskii, “O povedenii volnovodnykh matrits rasseyaniya v okrestnosti porogov”, Algebra analiz, 30:2 (2018), 188–237

[9] L. Bers, F. John, and M. Schechter, Partial Differential Equations, Interscience Publishers, New York–London–Sydney, 1964 | MR