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A multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations
Lin,Xue lei1; Ng,Michael K.2; Sun,Hai Wei1
2017-02-17
Source PublicationJournal of Computational Physics
ISSN10902716 00219991
Volume336Pages:69-86
Abstract

In this paper, we study a V-cycle multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations. The coefficient matrices of the linear systems are structured such that their matrix-vector multiplications can be computed efficiently. The main advantage using the multigrid method is to handle the space-fractional diffusion equations on non-rectangular domains, and to solve the linear systems with non-constant coefficients more effectively. The main idea of the proposed multigrid method is to employ two banded splitting iteration schemes as pre-smoother and post-smoother. The pre-smoother and the post-smoother take banded splitting of the coefficient matrix under the x-dominant ordering and the y-dominant ordering, respectively. We prove the convergence of the proposed two banded splitting iteration schemes in the sense of infinity norm. Results of numerical experiments for time-dependent two-dimensional space-fractional diffusion equations on rectangular, L-shape and U-shape domains are reported to demonstrate that both computational time and iteration number required by the proposed method are significantly smaller than those of the other tested methods.

KeywordBanded-splitting Smoother Fractional Diffusion Equation Multigrid Method Non-rectangular Domain
DOI10.1016/j.jcp.2017.02.008
URLView the original
Indexed BySCI
Language英语
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000397362800004
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Cited Times [WOS]:16   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
Personal research not belonging to the institution
Affiliation1.Department of MathematicsUniversity of Macau,Macao
2.Department of MathematicsHong Kong Baptist University,Hong Kong
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lin,Xue lei,Ng,Michael K.,Sun,Hai Wei. A multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations[J]. Journal of Computational Physics,2017,336:69-86.
APA Lin,Xue lei,Ng,Michael K.,&Sun,Hai Wei.(2017).A multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations.Journal of Computational Physics,336,69-86.
MLA Lin,Xue lei,et al."A multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations".Journal of Computational Physics 336(2017):69-86.
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