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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 8, Pages 1476–1489 (Mi zvmmf9528)  
This article is cited in 6 scientific papers (total in 6 papers)

Numerical methods for determining the inhomogeneity boundary in a boundary value problem for Laplace’s equation in a piecewise homogeneous medium

S. V. Gavrilov, A. M. Denisov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992 Russia
Full-text PDF (838 kB) Citations (6)
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Abstract: A boundary value problem for Laplace’s equation in a bounded two-dimensional domain filled with a piecewise homogeneous medium is considered. The boundary of the inhomogeneity is assumed to be unknown. The inverse problem of determining the inhomogeneity boundary and the solution of the equation given the solution and its normal derivative on the boundary of the domain is discussed. Numerical methods are proposed for solving the inverse problem, and the results of numerical experiments are presented.
Key words: Laplace’s equation, piecewise homogeneous medium, unknown boundary, inverse problem, numerical method.
Received: 17.02.2011
English version:
Computational Mathematics and Mathematical Physics, 2011, Volume 51, Issue 8, Pages 1377–1390
DOI: https://doi.org/10.1134/S0965542511080094
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: S. V. Gavrilov, A. M. Denisov, “Numerical methods for determining the inhomogeneity boundary in a boundary value problem for Laplace’s equation in a piecewise homogeneous medium”, Zh. Vychisl. Mat. Mat. Fiz., 51:8 (2011), 1476–1489; Comput. Math. Math. Phys., 51:8 (2011), 1377–1390
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Æóðíàë âû÷èñëèòåëüíîé ìàòåìàòèêè è ìàòåìàòè÷åñêîé ôèçèêè Computational Mathematics and Mathematical Physics
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