UM
A separable preconditioner for time-space fractional Caputo-Riesz diffusion equations
Lin,Xuelei1; Ng,Michael K.1; Sun,Haiwei2
2018
Source PublicationNumerical Mathematics
ISSN1004-8979
Volume11Issue:4Pages:827-853
AbstractIn 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 ε-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 Block ε-circulant preconditioner Diagonalization Separable Time-space fractional diffusion equations Toeplitz-like matrix
DOI10.4208/nmtma.2018.s09
URLView the original
Language英语
Scopus ID2-s2.0-85061877683
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Cited Times [WOS]:10   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorLin,Xuelei
Affiliation1.Department of Mathematics,Hong Kong Baptist University,Hong Kong
2.Department of Mathematics,University of Macau,Macao
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,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,11(4),827-853.
MLA Lin,Xuelei,et al."A separable preconditioner for time-space fractional Caputo-Riesz diffusion equations".Numerical Mathematics 11.4(2018):827-853.
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