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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 2, Pages 310–321
DOI: https://doi.org/10.7868/S0044466915020167 (Mi zvmmf10160) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Domain decomposition method for a model crack problem with a possible contact of crack edges

E. M. Rudoyab

a Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent’eva 15, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.7868/S0044466915020167
Abstract: The scalar Poisson equation is considered in a domain having a cut with unilateral constraints specified on its edges. An iterative method is proposed for solving the problem. The method is based on domain decomposition and the Uzawa algorithm for finding a saddle point of the Lagrangian. According to the method, the original domain is divided into two subdomains and a linear problem for Poisson’s equation is solved in each of them at every iteration step. The solution in one domain is related to that in the other by two Lagrange multipliers: one is used to match the solutions, and the other, to satisfy the unilateral constraint. Examples of the numerical solution of the problem are given.
Key words: scalar Poisson equation, theory of cracks, unilateral constraint, domain decomposition method, Lagrange multipliers, Uzawa algorithm.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00017
13-08-01097
Received: 24.06.2014
Revised: 05.08.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 2, Pages 305–316
DOI: https://doi.org/10.1134/S0965542515020165
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: E. M. Rudoy, “Domain decomposition method for a model crack problem with a possible contact of crack edges”, Zh. Vychisl. Mat. Mat. Fiz., 55:2 (2015), 310–321; Comput. Math. Math. Phys., 55:2 (2015), 305–316
Citation in format AMSBIB
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    • This publication is cited in the following 13 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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