Efficient Preconditioning Based on Scaled Tridiagonal and Toeplitz-like Splitting Iteration Method for Conservative Space Fractional Diffusion Equations

被引:0
作者
Guo, Xiaofeng [1 ,2 ]
机构
[1] Fudan Univ, Sch Data Sci, Shanghai 200433, Peoples R China
[2] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China
基金
中国国家自然科学基金;
关键词
conservative space fractional diffusion equation; iteration methods; preconditioner; Toeplitz-like; matrix splitting; SPECTRAL-ANALYSIS;
D O I
10.3390/math12152405
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The purpose of this work is to study the efficient numerical solvers for time-dependent conservative space fractional diffusion equations. Specifically, for the discretized Toeplitz-like linear system, we aim to study efficient preconditioning based on a matrix-splitting iteration method. We propose a scaled tridiagonal and Toeplitz-like splitting iteration method. Its asymptotic convergence property is first established. Further, based on the induced preconditioner, a fast circulant-like preconditioner is developed to accelerate the convergence of the Krylov Subspace iteration methods. Theoretical results suggest that the fast preconditioner can inherit the effectiveness of the original induced preconditioner. Numerical results also demonstrate its efficiency.
引用
收藏
页数:22
相关论文
共 30 条
[1]   On regularized Hermitian splitting iteration methods for solving discretized almost-isotropic spatial fractional diffusion equations [J].
Bai, Zhong-Zhi ;
Lu, Kang-Ya .
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2020, 27 (01)
[2]   Respectively scaled HSS iteration methods for solving discretized spatial fractional diffusion equations [J].
Bai, Zhong-Zhi .
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2018, 25 (05)
[3]   Diagonal and Toeplitz splitting iteration methods for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equations [J].
Bai, Zhong-Zhi ;
Lu, Kang-Ya ;
Pan, Jian-Yu .
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2017, 24 (04)
[4]   Block triangular and skew-Hermitian splitting methods for positive-definite linear systems [J].
Bai, ZZ ;
Golub, GH ;
Lu, LZ ;
Yin, JF .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2005, 26 (03) :844-863
[5]   Preconditioners for fractional diffusion equations based on the spectral symbol [J].
Barakitis, Nikos ;
Ekstrtom, Sven-Erik ;
Vassalos, Paris .
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2022, 29 (05)
[6]  
Chan R H F., 2007, An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)
[7]   Lopsided scaled HSS preconditioner for steady-state space-fractional diffusion equations [J].
Chen, Fang ;
Li, Tian-Yi ;
Muratova, Galina, V .
CALCOLO, 2021, 58 (02)
[8]   SPECTRAL ANALYSIS AND MULTIGRID METHODS FOR FINITE VOLUME APPROXIMATIONS OF SPACE-FRACTIONAL DIFFUSION EQUATIONS [J].
Donatelli, Marco ;
Mazza, Mariarosa ;
Serra-Capizzano, Stefano .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2018, 40 (06) :A4007-A4039
[9]   Spectral analysis and structure preserving preconditioners for fractional diffusion equations [J].
Donatelli, Marco ;
Mazza, Mariarosa ;
Serra-Capizzano, Stefano .
JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 307 :262-279
[10]   Evidence of one-dimensional scale-dependent fractional advection-dispersion [J].
Huang, GH ;
Huang, QZ ;
Zhan, HB .
JOURNAL OF CONTAMINANT HYDROLOGY, 2006, 85 (1-2) :53-71