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Fast ADI method for high dimensional fractional diffusion equations in conservative form with preconditioned strategy
Chou, Lot-Kei; Lei, Siu-Long
2017-02
Source PublicationCOMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN0898-1221
Volume73Issue:3Pages:385-403
Abstract

In this paper, high dimensional two-sided space fractional diffusion equations, derived from the fractional Fick's law, and with monotonic variable diffusion coefficients, are solved by alternating direction implicit method. Each linear system corresponding to each spatial direction thus resulted is solved by Krylov subspace method. The method is accelerated by applying an approximate inverse preconditioner, where under certain conditions we showed that the normalized preconditioned matrix is equal to a sum of identity matrix, a matrix with small norm, and a matrix with low rank, such that the preconditioned Krylov subspace method converges superlinearly. We also briefly present some fast algorithms whose computational cost for solving the linear systems is O(n log n), where n is the matrix size. The results are illustrated by some numerical examples. (C) 2016 Elsevier Ltd. All rights reserved.

KeywordHigh Dimensional Two-sided Fractional Diffusion Equation Alternating Direction Implicit Method Approximate Inverse Preconditioner Krylov Subspace Method Superlinear Convergence Fast Fourier Transform
DOI10.1016/j.camwa.2016.11.034
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000394199100003
PublisherPERGAMON-ELSEVIER SCIENCE LTD
The Source to ArticleWOS
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Citation statistics
Cited Times [WOS]:6   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
AffiliationUniv Macau, Dept Math, Ave Univ, Taipa, Macau, Peoples R China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Chou, Lot-Kei,Lei, Siu-Long. Fast ADI method for high dimensional fractional diffusion equations in conservative form with preconditioned strategy[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2017,73(3):385-403.
APA Chou, Lot-Kei,&Lei, Siu-Long.(2017).Fast ADI method for high dimensional fractional diffusion equations in conservative form with preconditioned strategy.COMPUTERS & MATHEMATICS WITH APPLICATIONS,73(3),385-403.
MLA Chou, Lot-Kei,et al."Fast ADI method for high dimensional fractional diffusion equations in conservative form with preconditioned strategy".COMPUTERS & MATHEMATICS WITH APPLICATIONS 73.3(2017):385-403.
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