Parallel multigrid method for solving inverse problems

We considered in this work the linear operator equation and used the Landweber iterative method as an iterative solver. After that, we used the multigrid method as an optimization method for obtaining an approximation solution with a highly accurate and fast process. A new parallel algorithm for the...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:MethodsX Jg. 9; S. 101887
Hauptverfasser: Al-Mahdawi, H.K., Sidikova, A. I, Alkattan, Hussein, Abotaleb, Mostafa, Kadi, Ammar, El-kenawy, El-Sayed M
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Netherlands Elsevier B.V 01.01.2022
Elsevier
Schlagworte:
Inverse problem
Iteration method
Method
Multigrid
Parallel
Parallel Multigrid Method
Parallel
Iteration method
Multigrid
Inverse problem
Parallel Multigrid Method
ISSN:2215-0161, 2215-0161
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We considered in this work the linear operator equation and used the Landweber iterative method as an iterative solver. After that, we used the multigrid method as an optimization method for obtaining an approximation solution with a highly accurate and fast process. A new parallel algorithm for the multigrid process has been developed. The proposed algorithm is based on a V-cycle mixed with the two-grid method. This modification of the V-cycle provides for parallel computing for each level. A coarse grid operator with a residual right-hand side vector for each coarse grid is provided. This parallel algorithm is used to accelerate and enhance computation for the solution of the iteration method in solving the inverse ill-posed problems. The necessary cost-time computation for all stages and processes for the parallel V-cycle algorithm has been done. A numerical experiment on solving the IVP (initial value problem) for the heat equation showed that the new parallel algorithm is much more efficient than the sequential method.•The study of iteration algorithms and mathematical experiments reveals a slow rate of convergence.•The Multigrid method is often used to speed up the rate of convergence of iterative methods, which is an effective method of solving large systems of linear algebra equations.•The approximation solution for the linear algebra equations was found by using the parallel method with the multigrid method. [Display omitted]
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:2215-0161
2215-0161
DOI:10.1016/j.mex.2022.101887