Geodesic
Fast iteration method in the problem of waves interacting with a set of thin screens
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 8, pp. 1374-1386

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A new iteration method is proposed for the wave equation describing the scattering of a harmonic wave from an arbitrary configuration in the form of an array of thin straight barriers. The problem is reduced to a system of boundary integral equations, which are discretized by applying the Belotserkovskii–Lifanov method. In discrete form, a finite number of systems with Toeplitz matrices (the number of systems is equal to the number of barriers) are solved at each iteration step by applying special fast methods. The algorithm is tested on several geometries, and its convergence in these cases is analyzed. 
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     author = {V. V. Popuzin and M. A. Sumbatyan and R. A. Tanyushin},
     title = {Fast iteration method in the problem of waves interacting with a set of thin screens},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1374--1386},
     publisher = {mathdoc},
     volume = {53},
     number = {8},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_8_a12/}
}
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V. V. Popuzin; M. A. Sumbatyan; R. A. Tanyushin. Fast iteration method in the problem of waves interacting with a set of thin screens. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 8, pp. 1374-1386. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_8_a12/