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Sibirskii Zhurnal Industrial'noi Matematiki, 2021, Volume 24, Number 2, Pages 134–147
DOI: https://doi.org/10.33048/SIBJIM.2021.24.211 (Mi sjim1136) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Direct method for solving the inverse coefficient problem for elliptic equation with piecewise constant coefficients

S. B. Sorokinab

a Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentyeva 6, Novosibirsk 630090, Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
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DOI: https://doi.org/10.33048/SIBJIM.2021.24.211
Abstract: Some direct numerical method is presented for solving the inverse coefficient problem for an elliptic equation with piecewise constant coefficients. It is assumed that the discontinuity points of the coefficients are known. The algorithm is based on the theory of spectral problems of linear algebra and the application of finite-difference methods for solving the elliptic equations. The values (measurements) of the solution at the discontinuity points of the coefficients are used as additional information. In the case of unperturbed additional information, the coefficients are reconstructed precisely.
Keywords: inverse coefficient problem, numerical solution, spectral problem, exact difference scheme, direct method. .
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0315-2019-0001
The author was supported by the State Task to the Institute of Computational Mathematics and Mathematical Geophysics (project no. 0251-2021-0001).
Received: 09.03.2021
Revised: 19.03.2021
Accepted: 15.04.2021
English version:
Journal of Applied and Industrial Mathematics, 2021, Volume 15, Issue 2, Pages 331–342
DOI: https://doi.org/10.1134/S1990478921020150
Bibliographic databases:
Document Type: Article
UDC: 519.632
Language: Russian
Citation: S. B. Sorokin, “Direct method for solving the inverse coefficient problem for elliptic equation with piecewise constant coefficients”, Sib. Zh. Ind. Mat., 24:2 (2021), 134–147; J. Appl. Industr. Math., 15:2 (2021), 331–342
Citation in format AMSBIB
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\by S.~B.~Sorokin
\paper Direct method for solving the inverse coefficient problem
for elliptic equation with piecewise constant coefficients
\jour Sib. Zh. Ind. Mat.
\yr 2021
\vol 24
\issue 2
\pages 134--147
\mathnet{http://mi.mathnet.ru/sjim1136}
\crossref{https://doi.org/10.33048/SIBJIM.2021.24.211}
\elib{https://elibrary.ru/item.asp?id=47508707}
\transl
\jour J. Appl. Industr. Math.
\yr 2021
\vol 15
\issue 2
\pages 331--342
\crossref{https://doi.org/10.1134/S1990478921020150}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85116268487}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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