DOI: https://doi.org/10.26089/NumMet.v23r417

Parallel sweep algorithm for solving direct and inverse problems for time-fractional diffusion equation

Authors

  • Elena N. Akimova
  • Murat A. Sultanov
  • Vladimir E. Misilov
  • Yerkebulan Nurlanuly

Keywords:

fractional diffusion equation
Caputo derivative
initial boundary problem
inverse problem
time-dependent right-hand part,
parallel sweep method
multicore processors
OpenMP

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.

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Published

2022-10-09

Issue

Vol. 23 (2022): Issue 4.

Section

Parallel software tools and technologies

Author Biographies

Elena N. Akimova

N.N. Krasovskii Institute of Mathematics and Mechanics of UB RAS (IMM UB RAS) ,
• Leading Researcher
Ural Federal University (UrFU)
• Professor

Murat A. Sultanov

Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkestan, Kazakhstan
• Professor

Vladimir E. Misilov

N.N. Krasovskii Institute of Mathematics and Mechanics of UB RAS (IMM UB RAS) ,
• Researcher
Ural Federal University (UrFU)
• Associate Professor

Yerkebulan Nurlanuly

Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkestan, Kazakhstan
• Doctoral Student

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Copyright (c) 2022 Е. Н. Акимова, М. А. Султанов, В. Е. Мисилов, Е. Нурланулы

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