Splitting preconditioning based on sine transform for time-dependent Riesz space fractional diffusion equations

We study the sine-transform-based splitting preconditioning technique for the linear systems arising in the numerical discretization of time-dependent one dimensional and two dimensional Riesz space fractional diffusion equations. Those linear systems are Toeplitz-like. By making use of diagonal-plu...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2021-06, Vol.66 (1-2), p.673-700
Main Authors: Lu, Xin, Fang, Zhi-Wei, Sun, Hai-Wei
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Clustering
Computational Mathematics and Numerical Analysis
Iterative methods
Linear systems
Mathematical analysis
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Original Research
Preconditioning
Splitting
Subspace methods
Theory of Computation
Time dependence
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Summary:We study the sine-transform-based splitting preconditioning technique for the linear systems arising in the numerical discretization of time-dependent one dimensional and two dimensional Riesz space fractional diffusion equations. Those linear systems are Toeplitz-like. By making use of diagonal-plus-Toeplitz splitting iteration technique, a sine-transform-based splitting preconditioner is proposed to accelerate the convergence rate efficiently when the Krylov subspace method is implemented. Theoretically, we prove that the spectrum of the preconditioned matrix of the proposed method is clustering around 1. In practical computations, by the fast sine transform the computational complexity at each time level can be done in O ( n log n ) operations where n is the matrix size. Numerical examples are presented to illustrate the effectiveness of the proposed algorithm.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-020-01454-0