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

Authors

DOI:

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

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.

Author Biographies

Elena N. Akimova

Murat A. Sultanov

Vladimir E. Misilov

Yerkebulan Nurlanuly

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Published

09-10-2022

How to Cite

Акимова Е. Н., Султанов М. А., Мисилов В. Е., Нурланулы Е. Parallel Sweep Algorithm for Solving Direct and Inverse Problems for Time-Fractional Diffusion Equation // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2022. 23. 275-287. doi 10.26089/NumMet.v23r417

Issue

Section

Parallel software tools and technologies