An efficient positive‐definite block‐preconditioned finite volume solver for two‐sided fractional diffusion equations on composite mesh
暂无分享,去创建一个
Qingbiao Wu | Jinhong Jia | Ping-Fei Dai | Hong Wang | Xiangcheng Zheng | Qingbiao Wu | Xiangcheng Zheng | Hong Wang | Ping-Fei Dai | J. Jia
[1] Zhiping Mao,et al. A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative , 2018, SIAM J. Numer. Anal..
[2] D. Benson,et al. The fractional‐order governing equation of Lévy Motion , 2000 .
[3] Fawang Liu,et al. A Crank-Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation , 2014, SIAM J. Numer. Anal..
[4] Hong Wang,et al. A direct O(N log2 N) finite difference method for fractional diffusion equations , 2010, J. Comput. Phys..
[5] Hongfei Fu,et al. Stability and convergence of a Crank–Nicolson finite volume method for space fractional diffusion equations , 2019, Applied Numerical Mathematics.
[6] Qingbiao Wu,et al. Quasi‐Toeplitz splitting iteration methods for unsteady space‐fractional diffusion equations , 2018, Numerical Methods for Partial Differential Equations.
[7] Daniele Bertaccini,et al. Limited Memory Block Preconditioners for Fast Solution of Fractional Partial Differential Equations , 2018, J. Sci. Comput..
[8] Fawang Liu,et al. A finite volume method for solving the two-sided time-space fractional advection-dispersion equation , 2012 .
[9] Norbert Heuer,et al. Regularity of the solution to 1-D fractional order diffusion equations , 2016, Math. Comput..
[10] Fawang Liu,et al. Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation , 2015, Appl. Math. Comput..
[11] Michael K. Ng,et al. Preconditioning Techniques for Diagonal-times-Toeplitz Matrices in Fractional Diffusion Equations , 2014, SIAM J. Sci. Comput..
[12] Owe Axelsson,et al. A new version of a preconditioning method for certain two-by-two block matrices with square blocks , 2018, BIT Numerical Mathematics.
[13] Hong Wang,et al. A Fast Finite Difference Method for Two-Dimensional Space-Fractional Diffusion Equations , 2012, SIAM J. Sci. Comput..
[14] Daniele Bertaccini,et al. Block structured preconditioners in tensor form for the all-at-once solution of a finite volume fractional diffusion equation , 2019, Appl. Math. Lett..
[15] Hong Wang,et al. A preconditioned fast finite volume scheme for a fractional differential equation discretized on a locally refined composite mesh , 2015, J. Comput. Phys..
[16] T. Chan. An Optimal Circulant Preconditioner for Toeplitz Systems , 1988 .
[17] Raymond H. Chan,et al. Conjugate Gradient Methods for Toeplitz Systems , 1996, SIAM Rev..
[18] Vickie E. Lynch,et al. Fractional diffusion in plasma turbulence , 2004 .
[19] William Rundell,et al. Variational formulation of problems involving fractional order differential operators , 2013, Math. Comput..
[20] Weihua Deng,et al. Finite Element Method for the Space and Time Fractional Fokker-Planck Equation , 2008, SIAM J. Numer. Anal..
[21] Qianqian Yang,et al. A finite volume method for two-sided fractional diffusion equations on non-uniform meshes , 2017, J. Comput. Phys..
[22] Stefano Serra Capizzano,et al. Spectral analysis and structure preserving preconditioners for fractional diffusion equations , 2016, J. Comput. Phys..
[23] Xiangcheng Zheng,et al. Spectral approximation of a variable coefficient fractional diffusion equation in one space dimension , 2018, Appl. Math. Comput..
[24] A Fast Finite Volume Method on Locally Refined Meshes for Fractional Diffusion Equations , 2019, East Asian Journal on Applied Mathematics.
[25] Xiao-Qing Jin,et al. Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations , 2015 .
[26] G. Strang. A proposal for toeplitz matrix calculations , 1986 .
[27] V. Ervin,et al. Variational formulation for the stationary fractional advection dispersion equation , 2006 .
[28] Zhong-Zhi Bai,et al. Diagonal and Toeplitz splitting iteration methods for diagonal‐plus‐Toeplitz linear systems from spatial fractional diffusion equations , 2017, Numer. Linear Algebra Appl..
[29] David A. Benson,et al. Space‐fractional advection‐dispersion equations with variable parameters: Diverse formulas, numerical solutions, and application to the Macrodispersion Experiment site data , 2007 .
[30] Stefano Serra Capizzano,et al. Spectral Analysis and Multigrid Methods for Finite Volume Approximations of Space-Fractional Diffusion Equations , 2018, SIAM J. Sci. Comput..
[31] S. K. Bhowmik,et al. Preconditioners based on windowed Fourier frames applied to elliptic partial differential equations , 2010, 1009.1925.
[32] Martin Stoll,et al. Fast iterative solvers for fractional dierential equations , 2014 .
[33] Hong Wang,et al. Fast Iterative Solvers for Linear Systems Arising from Time-Dependent Space-Fractional Diffusion Equations , 2016, SIAM J. Sci. Comput..