A separable preconditioner for time-space fractional Caputo-Riesz di usion equations

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	A separable preconditioner for time-space fractional Caputo-Riesz di usion equations
	Lin, X.L.; Ng, M.K.; Sun, H. W.
	2018-11-01
Source Publication	Numerical Mathematics: Theory, Methods and Applications
ISSN	1004-8979
Pages	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 coefficients 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 -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.
Keyword	Block lower triangular Toeplitz-like matrix Diagonalization Separable Block \epsilon-circulant preconditioner Time-space fractional diffusion equations
Language	英語English
The Source to Article	PB_Publication
PUB ID	35306
Document Type	Journal article
Collection	DEPARTMENT OF MATHEMATICS
Corresponding Author	Sun, H. W.
Recommended Citation GB/T 7714	Lin, X.L.,Ng, M.K.,Sun, H. W.. A separable preconditioner for time-space fractional Caputo-Riesz di usion equations[J]. Numerical Mathematics: Theory, Methods and Applications, 2018, 827-853.
APA	Lin, X.L.., Ng, M.K.., & Sun, H. W. (2018). A separable preconditioner for time-space fractional Caputo-Riesz di usion equations. Numerical Mathematics: Theory, Methods and Applications, 827-853.
MLA	Lin, X.L.,et al."A separable preconditioner for time-space fractional Caputo-Riesz di usion equations".Numerical Mathematics: Theory, Methods and Applications (2018):827-853.

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