A quadratic spline collocation method combined with the Crank-Nicolson time discretization of the space fractional diffusion equations gives discrete linear systems,whose coefficient matrix is the sum of a tridiagonal...A quadratic spline collocation method combined with the Crank-Nicolson time discretization of the space fractional diffusion equations gives discrete linear systems,whose coefficient matrix is the sum of a tridiagonal matrix and two diagonalmultiply-Toeplitz-like matrices.By exploiting the Toeplitz-like structure,we split the Toeplitz-like matrix as the sum of a Toeplitz matrix and a rank-2 matrix and Strang’s circulant preconditioner is constructed to accelerate the convergence of Krylov subspace method like generalized minimal residual method for solving the discrete linear systems.In theory,both the invertibility of the proposed preconditioner and the clustering spectrum of the corresponding preconditioned matrix are discussed in detail.Finally,numerical results are given to demonstrate that the performance of the proposed preconditioner is better than that of the generalized T.Chan’s circulant preconditioner proposed recently by Liu et al.(J.Comput.Appl.Math.,360(2019),pp.138–156)for solving the discrete linear systems of one-dimensional and two-dimensional space fractional diffusion equations.展开更多
基金supported by the research grants MYRG2020-00208-FST from University of Macao2020A1515110454 from Guangdong Basic and Applied Basic Research Foundation+2 种基金2021KCXTD052 from the Scientific Computing Research Innovation Team of Guangdong Provincesupported by the research grant 0118/2018/A3 from Macao Science and Technology Development Fund(FDCT)supported by the research grants MYRG2020-00208-FST and MYRG2022-00262-FST from University of Macao.
文摘A quadratic spline collocation method combined with the Crank-Nicolson time discretization of the space fractional diffusion equations gives discrete linear systems,whose coefficient matrix is the sum of a tridiagonal matrix and two diagonalmultiply-Toeplitz-like matrices.By exploiting the Toeplitz-like structure,we split the Toeplitz-like matrix as the sum of a Toeplitz matrix and a rank-2 matrix and Strang’s circulant preconditioner is constructed to accelerate the convergence of Krylov subspace method like generalized minimal residual method for solving the discrete linear systems.In theory,both the invertibility of the proposed preconditioner and the clustering spectrum of the corresponding preconditioned matrix are discussed in detail.Finally,numerical results are given to demonstrate that the performance of the proposed preconditioner is better than that of the generalized T.Chan’s circulant preconditioner proposed recently by Liu et al.(J.Comput.Appl.Math.,360(2019),pp.138–156)for solving the discrete linear systems of one-dimensional and two-dimensional space fractional diffusion equations.
