Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term
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| Автор |
Akimova, E. N.
Sultanov, M. A. Misilov, V. E. Nurlanuly, Y. |
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| Тематика |
BLOCK-ELIMINATION METHOD
CAPUTO FRACTIONAL DERIVATIVE FINITE-DIFFERENCE SCHEME INVERSE PROBLEMS PARALLEL COMPUTING PARALLEL MATRIX SWEEP METHOD SOURCE TERM IDENTIFICATION TIME-FRACTIONAL DIFFUSION EQUATION |
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| Описание |
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. © 2023 by the authors.
Ministry of Education and Science of the Republic of Kazakhstan: AP09258836 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. |
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| Дата |
2024-04-05T16:37:12Z
2024-04-05T16:37:12Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
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
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 2504-3110 Final All Open Access, Gold https://www.scopus.com/inward/record.uri?eid=2-s2.0-85178308640&doi=10.3390%2ffractalfract7110801&partnerID=40&md5=18afeb3474e8041108924ecdac9b866d https://www.mdpi.com/2504-3110/7/11/801/pdf?version=1698915587 http://elar.urfu.ru/handle/10995/131016 10.3390/fractalfract7110801 85178308640 001109795200001 |
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| Язык |
en
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| Права |
Open access (info:eu-repo/semantics/openAccess)
cc-by https://creativecommons.org/licenses/by/4.0/ |
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| Формат |
application/pdf
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| Издатель |
Multidisciplinary Digital Publishing Institute (MDPI)
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| Источник |
Fractal and Fractional
Fractal and Fractional |
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