A Direct Method for Solving the Inverse Coefficient Problem for an Elliptic Equation with Piecewise Constant Coefficients

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A Direct Method for Solving the Inverse Coefficient Problem for an Elliptic Equation with Piecewise Constant Coefficients. / Sorokin, S. B.

In: Journal of Applied and Industrial Mathematics, Vol. 15, No. 2, 04.2021, p. 331-342.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{1dbac5add185465eb36ada1dceb1074e,

title = "A Direct Method for Solving the Inverse Coefficient Problem for an Elliptic Equation with Piecewise Constant Coefficients",

abstract = "Some direct numerical method is presented for solving the inverse coefficient problem foran elliptic equation with piecewise constant coefficients. The discontinuity points of thecoefficients are assumed known. The algorithm is based on the theory of spectral problems oflinear algebra and the application of finite-difference methods for solving elliptic equations. Thevalues (measurements) of the solution at the discontinuity points of the coefficients are used asadditional information. In the case of unperturbed additional information, the coefficients arereconstructed precisely.",

keywords = "direct method, exact difference scheme, inverse coefficient problem, numerical solution, spectral problem",

author = "Sorokin, {S. B.}",

note = "Funding Information: The author was supported by the State Task to the Institute of Computational Mathematics and Mathematical Geophysics (project no. 0251–2021–0001). Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = apr,

doi = "10.1134/S1990478921020150",

language = "English",

volume = "15",

pages = "331--342",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - A Direct Method for Solving the Inverse Coefficient Problem for an Elliptic Equation with Piecewise Constant Coefficients

AU - Sorokin, S. B.

N1 - Funding Information: The author was supported by the State Task to the Institute of Computational Mathematics and Mathematical Geophysics (project no. 0251–2021–0001). Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/4

Y1 - 2021/4

N2 - Some direct numerical method is presented for solving the inverse coefficient problem foran elliptic equation with piecewise constant coefficients. The discontinuity points of thecoefficients are assumed known. The algorithm is based on the theory of spectral problems oflinear algebra and the application of finite-difference methods for solving elliptic equations. Thevalues (measurements) of the solution at the discontinuity points of the coefficients are used asadditional information. In the case of unperturbed additional information, the coefficients arereconstructed precisely.

AB - Some direct numerical method is presented for solving the inverse coefficient problem foran elliptic equation with piecewise constant coefficients. The discontinuity points of thecoefficients are assumed known. The algorithm is based on the theory of spectral problems oflinear algebra and the application of finite-difference methods for solving elliptic equations. Thevalues (measurements) of the solution at the discontinuity points of the coefficients are used asadditional information. In the case of unperturbed additional information, the coefficients arereconstructed precisely.

KW - direct method

KW - exact difference scheme

KW - inverse coefficient problem

KW - numerical solution

KW - spectral problem

UR - http://www.scopus.com/inward/record.url?scp=85116268487&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/6c5399d0-be22-332e-ad4a-313e1c89dddd/

U2 - 10.1134/S1990478921020150

DO - 10.1134/S1990478921020150

M3 - Article

AN - SCOPUS:85116268487

VL - 15

SP - 331

EP - 342

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 2

ER -

ID: 34400774