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Preconditioners with Symmetrized Techniques for Space Fractional Cahn-Hilliard Equations
Huang, Xin1; Li, Dongfang1,2; Sun, Hai Wei3; Zhang, Fan3
2022-08-01
Source PublicationJournal of Scientific Computing
ISSN0885-7474
Volume92Issue:2
Abstract

In this paper, we study space fractional Cahn-Hilliard equations. A second-order stabilized finite difference scheme is exploited for the model equations. The resulting coefficient matrix is a nonsymmetric ill-conditioned Toeplitz-like matrix. Symmetrized strategies are proposed for the nonsymmetric system so that the conjugate gradient method can be utilized to derive the numerical solutions. Moreover, preconditioners based on the sine transform are designed to speed up the convergence rate of the proposed methods. Theoretically, we prove that the spectra of the preconditioned matrices are uniformly bounded in the interval (1/2, 3/2), which guarantees that the preconditioned conjugate gradient method converges linearly, within an iteration number independent of the matrix size. Numerical experiments are reported to show the effectiveness of the proposed methods.

KeywordConjugate Gradient Method Fast Algorithm Fractional Cahn-hilliard Sine Transform Based Preconditioner Toeplitz-like
DOI10.1007/s10915-022-01900-0
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000819018300002
Scopus ID2-s2.0-85132992729
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Cited Times [WOS]:0   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorSun, Hai Wei
Affiliation1.School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China
2.Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China
3.Department of Mathematics, University of Macau, Macao
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Huang, Xin,Li, Dongfang,Sun, Hai Wei,et al. Preconditioners with Symmetrized Techniques for Space Fractional Cahn-Hilliard Equations[J]. Journal of Scientific Computing,2022,92(2).
APA Huang, Xin,Li, Dongfang,Sun, Hai Wei,&Zhang, Fan.(2022).Preconditioners with Symmetrized Techniques for Space Fractional Cahn-Hilliard Equations.Journal of Scientific Computing,92(2).
MLA Huang, Xin,et al."Preconditioners with Symmetrized Techniques for Space Fractional Cahn-Hilliard Equations".Journal of Scientific Computing 92.2(2022).
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