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Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term. / Akimova, Elena n.; Sultanov, Murat A.; Misilov, Vladimir E. и др.
в: Fractal and Fractional, Том 7, № 11, 801, 2023.

Результаты исследований: Вклад в журнал › Статья › Рецензирование

Harvard

Akimova, EN, Sultanov, MA, Misilov, VE & Nurlanuly, Y 2023, 'Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term', Fractal and Fractional, Том. 7, № 11, 801. https://doi.org/10.3390/fractalfract7110801

APA

Akimova, E. N., Sultanov, M. A., Misilov, V. E., & Nurlanuly, Y. (2023). Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term. Fractal and Fractional, 7(11), [801]. https://doi.org/10.3390/fractalfract7110801

Vancouver

Akimova EN, Sultanov MA, Misilov VE, Nurlanuly Y. Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term. Fractal and Fractional. 2023;7(11):801. doi: 10.3390/fractalfract7110801

Author

Akimova, Elena n. ; Sultanov, Murat A. ; Misilov, Vladimir E. и др. / Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term. в: Fractal and Fractional. 2023 ; Том 7, № 11.

BibTeX

@article{528f5babd14b47a480b2765c9be5bd40,
title = "Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term",
abstract = "This paper is devoted to the development of a parallel algorithm for solving the inverse problem of identifying the space-dependent source term in the two-dimensional fractional diffusion equation. For solving the inverse problem, the regularized iterative conjugate gradient method is used. At each iteration of the method, we need to solve the auxilliary direct initial-boundary value problem. By using the finite difference scheme, this problem is reduced to solving a large system of a linear algebraic equation with a block-tridiagonal matrix at each time step. Solving the system takes almost the entire computation time. To solve this system, we construct and implement the direct parallel matrix sweep algorithm. We establish stability and correctness for this algorithm. The parallel implementations are developed for the multicore CPU using the OpenMP technology. The numerical experiments are performed to study the performance of parallel implementations.",
author = "Akimova, {Elena n.} and Sultanov, {Murat A.} and Misilov, {Vladimir E.} and Yerkebulan Nurlanuly",
note = "The second author (M.A.S.) and fourth author (Y.N.) were financially supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan (project AP09258836). The first author (E.N.A.) and third author (V.E.M.) received no external funding.",
year = "2023",
doi = "10.3390/fractalfract7110801",
language = "English",
volume = "7",
journal = "Fractal and Fractional",
issn = "2504-3110",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "11",

}

RIS

TY - JOUR

T1 - Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term

AU - Akimova, Elena n.

AU - Sultanov, Murat A.

AU - Misilov, Vladimir E.

AU - Nurlanuly, Yerkebulan

N1 - The second author (M.A.S.) and fourth author (Y.N.) were financially supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan (project AP09258836). The first author (E.N.A.) and third author (V.E.M.) received no external funding.

PY - 2023

Y1 - 2023

N2 - This paper is devoted to the development of a parallel algorithm for solving the inverse problem of identifying the space-dependent source term in the two-dimensional fractional diffusion equation. For solving the inverse problem, the regularized iterative conjugate gradient method is used. At each iteration of the method, we need to solve the auxilliary direct initial-boundary value problem. By using the finite difference scheme, this problem is reduced to solving a large system of a linear algebraic equation with a block-tridiagonal matrix at each time step. Solving the system takes almost the entire computation time. To solve this system, we construct and implement the direct parallel matrix sweep algorithm. We establish stability and correctness for this algorithm. The parallel implementations are developed for the multicore CPU using the OpenMP technology. The numerical experiments are performed to study the performance of parallel implementations.

AB - This paper is devoted to the development of a parallel algorithm for solving the inverse problem of identifying the space-dependent source term in the two-dimensional fractional diffusion equation. For solving the inverse problem, the regularized iterative conjugate gradient method is used. At each iteration of the method, we need to solve the auxilliary direct initial-boundary value problem. By using the finite difference scheme, this problem is reduced to solving a large system of a linear algebraic equation with a block-tridiagonal matrix at each time step. Solving the system takes almost the entire computation time. To solve this system, we construct and implement the direct parallel matrix sweep algorithm. We establish stability and correctness for this algorithm. The parallel implementations are developed for the multicore CPU using the OpenMP technology. The numerical experiments are performed to study the performance of parallel implementations.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85178308640

UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=001109795200001

U2 - 10.3390/fractalfract7110801

DO - 10.3390/fractalfract7110801

M3 - Article

VL - 7

JO - Fractal and Fractional

JF - Fractal and Fractional

SN - 2504-3110

IS - 11

M1 - 801

ER -

ID: 49270200