A Separable Preconditioner for Time-Space Fractional Caputo-Riesz Diffusion Equations

被引:18
作者
Lin, Xuelei [1 ]
Ng, Michael K. [1 ]
Sun, Haiwei [2 ]
机构
[1] Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China
[2] Univ Macau, Dept Math, Taipa, Macao, Peoples R China
关键词
Block lower triangular; Toeplitz-like matrix; diagonalization; separable; block is an element of-circulant preconditioner; time-space fractional diffusion equations; FINITE-DIFFERENCE SCHEMES; ANOMALOUS DIFFUSION; CIRCULANT PRECONDITIONER; MULTIGRID METHOD; APPROXIMATIONS;
D O I
10.4208/nmtma.2018.s09
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:827 / 853
页数:27
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