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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 395–410
DOI: https://doi.org/10.17377/semi.2016.13.035 (Mi semr684) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Differentical equations, dynamical systems and optimal control

Domain decomposition method for a membrane with a delaminated thin rigid inclusion

E. M. Rudoyab, V. V. Shcherbakovab

a Lavrentyev Institute of Hydrodynamics of the Russian Academy of Sciences, pr. Lavrenyeva, 15, 630090, Novosibirsk, Russia
b Novosibirsk State University, ul. Pirogova, 2, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/semi.2016.13.035
Abstract: The paper deals with the numerical solution of an equilibrium problem for an elastic membrane with a thin rigid inclusion. The thin inclusion is supposed to delaminate, therefore a crack between the inclusion and the membrane is considered. The boundary conditions for nonpenetration of the crack faces are fulfilled. We provide the relaxation of the problem and propose an iterative method for the numerical solution of the approximated problem. The method is based on a domain decomposition and the Uzawa algorithm for finding a saddle point of the Lagrangian. Examples of the numerical solution of the initial problem are presented.
Keywords: crack, thin rigid inclusion, nonpenetration condition, variational inequality, domain decomposition method, Uzawa algorithm.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation MD-3123.2015.1
The author is supported by the Grant of the President of the Russian Federation for state support of young Russian researchers (Grant No. MD-3123.2015.1).
Received March 10, 2016, published May 22, 2016
Bibliographic databases:
Document Type: Article
UDC: 519.63
MSC: 65N55, 65K15, 35Q74, 74R10, 35J50
Language: English
Citation: E. M. Rudoy, V. V. Shcherbakov, “Domain decomposition method for a membrane with a delaminated thin rigid inclusion”, Sib. Èlektron. Mat. Izv., 13 (2016), 395–410
Citation in format AMSBIB
\Bibitem{RudShc16}
\by E.~M.~Rudoy, V.~V.~Shcherbakov
\paper Domain decomposition method for a membrane with a delaminated thin rigid inclusion
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 395--410
\mathnet{http://mi.mathnet.ru/semr684}
\crossref{https://doi.org/10.17377/semi.2016.13.035}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000407781100035}
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  • https://www.mathnet.ru/eng/semr/v13/p395
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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