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This article is cited in 1 scientific paper (total in 1 paper)
Parallel software tools and technologies
Parallel sweep algorithm for solving direct and inverse problems for time-fractional diffusion equation
E. N. Akimovaab, M. A. Sultanovc, V. E. Misilovba, Y. Nurlanulyc a Ural Federal University, Ekaterinburg, Russia
b Krasovskii Institute of Mathematics and Mechanics, Ural Branch of RAS, Ekaterinburg, Russia
c Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkestan, Kazakhstan
Abstract:
The work is devoted to construction of parallel algorithm for solving the direct initial boundary and inverse right-hand part identification problems for the time-fractional diffusion equation. Application of a priori information on the solution at the some inner point allows one to reduce the inverse problem to an initial boundary problem for the auxiliary equation. After applying the finite-difference scheme the problems are reduced to solving systems of linear algebraic equations. The developed algorithms are based on the parallel sweep method and implemented for the multicore processor using the OpenMP technology. Numerical experiments were performed to study the performance of the developed algorithms.
Keywords:
fractional diffusion equation, Caputo derivative, initial boundary problem, inverse
problem, time-dependent right-hand part, parallel sweep method, multicore processors, OpenMP.
Received: 16.08.2022 Accepted: 14.09.2022
Citation:
E. N. Akimova, M. A. Sultanov, V. E. Misilov, Y. Nurlanuly, “Parallel sweep algorithm for solving direct and inverse problems for time-fractional diffusion equation”, Num. Meth. Prog., 23:4 (2022), 275–287
Linking options:
https://www.mathnet.ru/eng/vmp1062 https://www.mathnet.ru/eng/vmp/v23/i4/p275
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