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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 8, Pages 1374–1386
DOI: https://doi.org/10.7868/S0044466913060161 (Mi zvmmf9907) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Fast iteration method in the problem of waves interacting with a set of thin screens

V. V. Popuzina, M. A. Sumbatyanb, R. A. Tanyushinb

a 95125 Viale A. Doria, 6, Catania, Italy D.M.I. University of Catania
b Southern Federal University, Faculty of Mathematics, Mechanics and Computer Sciences
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DOI: https://doi.org/10.7868/S0044466913060161
Abstract: 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.
Key words: wave processes, thin barriers, boundary integral equations, fast algorithm, iteration method, Toeplitz matrix.
Received: 07.08.2012
Revised: 21.12.2012
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 8, Pages 1195–1206
DOI: https://doi.org/10.1134/S0965542513060158
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: V. V. Popuzin, M. A. Sumbatyan, R. A. Tanyushin, “Fast iteration method in the problem of waves interacting with a set of thin screens”, Zh. Vychisl. Mat. Mat. Fiz., 53:8 (2013), 1374–1386; Comput. Math. Math. Phys., 53:8 (2013), 1195–1206
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf/v53/i8/p1374
    • This publication is cited in the following 1 articles:
    1. D. A. Budzko, A. Cordero, J. R. Torregrosa, “New family of iterative methods based on the Ermakov–Kalitkin scheme for solving nonlinear systems of equations”, Comput. Math. Math. Phys., 55:12 (2015), 1947–1959  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Abstract page:222
    Full-text PDF :95
    References:46
    First page:12
     
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