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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 5, Pages 809–822
DOI: https://doi.org/10.31857/S0044466922050118
(Mi zvmmf11398)
 

This article is cited in 1 scientific paper (total in 1 paper)

Partial Differential Equations

Solution of the exterior boundary value problem for the Helmholtz equation using overlapping domain decomposition

A. V. Petukhov, A. O. Savchenko

Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences, 630090, Novosibirsk, Russia
Citations (1)
Abstract: A method for solving the exterior three-dimensional boundary value problem for the Helmholtz equation is proposed and investigated. The method is based on an overlapping decomposition of the external domain and on the Schwarz alternating method with the successive solution of the interior and exterior boundary value problem in overlapping subdomains on the adjacent boundaries of which iterated interface conditions are set. Sufficient conditions for the convergence of the method in the case of a negative coefficient in the Helmholtz equation are found. Convergence of a special case of the problem is analyzed, and conclusion on the applicability of the proposed approach to solving problems with an arbitrary wave number is drawn. The proposed method is successfully applied in combination with the finite volume method to the numerical solution of interior boundary value problems and in combination with Green’s formula for solving exterior boundary value problems. The convergence rate of the iterations and the accuracy of computations is illustrated by a series of computational experiments. The choice of decomposition parameters that ensure the convergence of the method is analyzed.
Key words: Helmholtz equation, exterior boundary value problem, domain decomposition, Green's formula.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 0251-2021-0001
This work was accomplished within the state assignment of the Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences, project no. 0251-2021-0001.
Received: 05.03.2020
Revised: 20.07.2021
Accepted: 14.01.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 5, Pages 784–796
DOI: https://doi.org/10.1134/S0965542522050116
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: A. V. Petukhov, A. O. Savchenko, “Solution of the exterior boundary value problem for the Helmholtz equation using overlapping domain decomposition”, Zh. Vychisl. Mat. Mat. Fiz., 62:5 (2022), 809–822; Comput. Math. Math. Phys., 62:5 (2022), 784–796
Citation in format AMSBIB
\Bibitem{PetSav22}
\by A.~V.~Petukhov, A.~O.~Savchenko
\paper Solution of the exterior boundary value problem for the Helmholtz equation using overlapping domain decomposition
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 5
\pages 809--822
\mathnet{http://mi.mathnet.ru/zvmmf11398}
\crossref{https://doi.org/10.31857/S0044466922050118}
\elib{https://elibrary.ru/item.asp?id=48506053}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 5
\pages 784--796
\crossref{https://doi.org/10.1134/S0965542522050116}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85132156543}
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  • https://www.mathnet.ru/eng/zvmmf/v62/i5/p809
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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