UM  > Faculty of Science and Technology  > DEPARTMENT OF MATHEMATICS
Affiliated with RCfalse
Status已發表Published
A Separable Preconditioner for Time-Space Fractional Caputo-Riesz Diffusion Equations
Lin, Xuelei1; Ng, Michael K.1; Sun, Haiwei2
2018-11
Source PublicationNUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN1004-8979
Volume11Issue:4Pages:827-853
Abstract

In this paper, we study linear systems arising from time-space fractional Caputo-Riesz diffusion equations with time-dependent diffusion coefficients. The coefficient matrix is a summation of a block-lower-triangular-Toeplitz matrix (temporal component) and a block-diagonal-with-diagonal-times-Toeplitz-block matrix (spatial component). The main aim of this paper is to propose separable preconditioners for solving these linear systems, where a block is an element of-circulant preconditioner is used for the temporal component, while a block diagonal approximation is used for the spatial variable. The resulting preconditioner can be block-diagonalized in the temporal domain. Furthermore, the fast solvers can be employed to solve smaller linear systems in the spatial domain. Theoretically, we show that if the diffusion coefficient (temporal-dependent or spatial-dependent only) function is smooth enough, the singular values of the preconditioned matrix are bounded independent of discretization parameters. Numerical examples are tested to show the performance of proposed preconditioner.

KeywordBlock Lower Triangular Toeplitz-like Matrix Diagonalization Separable Block Is An Element of-circulAnt Preconditioner Time-space Fractional Diffusion Equations
DOI10.4208/nmtma.2018.s09
URLView the original
Indexed BySCIE ; CPCI-S
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000438884900010
PublisherGLOBAL SCIENCE PRESS
The Source to ArticleWOS
Scopus ID2-s2.0-85061877683
Fulltext Access
Citation statistics
Cited Times [WOS]:12   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorLin, Xuelei; Ng, Michael K.; Sun, Haiwei
Affiliation1.Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China
2.Univ Macau, Dept Math, Taipa, Macao, Peoples R China
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lin, Xuelei,Ng, Michael K.,Sun, Haiwei. A Separable Preconditioner for Time-Space Fractional Caputo-Riesz Diffusion Equations[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2018,11(4):827-853.
APA Lin, Xuelei,Ng, Michael K.,&Sun, Haiwei.(2018).A Separable Preconditioner for Time-Space Fractional Caputo-Riesz Diffusion Equations.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,11(4),827-853.
MLA Lin, Xuelei,et al."A Separable Preconditioner for Time-Space Fractional Caputo-Riesz Diffusion Equations".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 11.4(2018):827-853.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Lin, Xuelei]'s Articles
[Ng, Michael K.]'s Articles
[Sun, Haiwei]'s Articles
Baidu academic
Similar articles in Baidu academic
[Lin, Xuelei]'s Articles
[Ng, Michael K.]'s Articles
[Sun, Haiwei]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Lin, Xuelei]'s Articles
[Ng, Michael K.]'s Articles
[Sun, Haiwei]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.