An efficient positive‐definite block‐preconditioned finite volume solver for two‐sided fractional diffusion equations on composite mesh

[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..