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Two-parameter modified matrix splitting iteration method for Helmholtz equation
Li, Tian Yi1; Chen, Fang2; Fang, Zhi Wei3; Sun, Hai Wei1; Wang, Zhi4
2024
Source PublicationInternational Journal of Computer Mathematics
ISSN0020-7160
Abstract

For effectively solving the nonsymmetric and indefinite linear system originating from the discretized Helmholtz equation with complex wavenumber, we propose a two-parameter modified matrix splitting iteration method. We establish the asymptotic convergence theory for this method and demonstrate its convergence under certain conditions. The proposed iteration method leads to a new preconditioner that can be efficiently inverted by using the discrete sine transform. Numerical experiments are carried out to show that the new preconditioner significantly improves the convergence rate of the GMRES method, which results in effective preconditioned GMRES method for solving the Helmholtz equation of high wavenumber.

KeywordComplex Linear System Convergence Property Helmholtz Equation Matrix Splitting Iteration Preconditioning
DOI10.1080/00207160.2023.2301570
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:001137436300001
PublisherTAYLOR & FRANCIS LTD, 2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND
Scopus ID2-s2.0-85181503307
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Citation statistics
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorSun, Hai Wei
Affiliation1.Department of Mathematics, University of Macau, Macao
2.School of Applied Science, Beijing Information Science and Technology University, Beijing, China
3.School of Mathematics and Big Data, Foshan University, Foshan, China
4.Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, China
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Li, Tian Yi,Chen, Fang,Fang, Zhi Wei,et al. Two-parameter modified matrix splitting iteration method for Helmholtz equation[J]. International Journal of Computer Mathematics, 2024.
APA Li, Tian Yi., Chen, Fang., Fang, Zhi Wei., Sun, Hai Wei., & Wang, Zhi (2024). Two-parameter modified matrix splitting iteration method for Helmholtz equation. International Journal of Computer Mathematics.
MLA Li, Tian Yi,et al."Two-parameter modified matrix splitting iteration method for Helmholtz equation".International Journal of Computer Mathematics (2024).
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