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A Separable Preconditioner for Time-Space Fractional Caputo-Riesz Diffusion Equations
Lin, Xuelei1; Ng, Michael K.1; Sun, Haiwei2
2018-11
Conference NameNUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
Source PublicationNUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
Volume11
Issue4
Pages827-853
Conference DateMAY 20-22, 2017
Conference PlaceUniv Macau, Macau, PEOPLES R CHINA
Publication PlaceROOM 3208, CENTRAL PLAZA, 18 HARBOUR RD, WANCHAI, HONG KONG 00000, PEOPLES R CHINA
PublisherGLOBAL SCIENCE PRESS
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
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000438884900010
The Source to ArticleWOS
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Cited Times [WOS]:10   [WOS Record]     [Related Records in WOS]
Document TypeConference paper
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China
2.Univ Macau, Dept Math, Taipa, Macao, Peoples R China
Recommended Citation
GB/T 7714
Lin, Xuelei,Ng, Michael K.,Sun, Haiwei. A Separable Preconditioner for Time-Space Fractional Caputo-Riesz Diffusion Equations[C]. ROOM 3208, CENTRAL PLAZA, 18 HARBOUR RD, WANCHAI, HONG KONG 00000, PEOPLES R CHINA:GLOBAL SCIENCE PRESS,2018:827-853.
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