Efficient ADI schemes and preconditioning for a class of high-dimensional spatial fractional diffusion equations with variable diffusion coefficients
DOI10.1016/j.cam.2022.114938zbMath1505.65284OpenAlexW4309633462MaRDI QIDQ2112673
Publication date: 11 January 2023
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2022.114938
fast Fourier transformToeplitz matrixKrylov subspace methodalternating direction implicit methodapproximate inverse preconditionerhigh-dimensional fractional diffusion equations
Fractional derivatives and integrals (26A33) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Iterative numerical methods for linear systems (65F10) Numerical methods for discrete and fast Fourier transforms (65T50) Finite difference methods for boundary value problems involving PDEs (65N06) Toeplitz, Cauchy, and related matrices (15B05) Preconditioners for iterative methods (65F08) Fractional partial differential equations (35R11) Numerical methods for low-rank matrix approximation; matrix compression (65F55)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Fractional Sturm-Liouville problem
- Fractional Sturm-Liouville eigen-problems: theory and numerical approximation
- Fast alternating-direction finite difference methods for three-dimensional space-fractional diffusion equations
- Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
- Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients
- Matrix approach to discrete fractional calculus. II: Partial fractional differential equations
- A lower bound for the smallest singular value of a matrix
- Four short stories about Toeplitz matrix calculations
- Stability and convergence analysis of finite difference schemes for time-dependent space-fractional diffusion equations with variable diffusion coefficients
- Circulant preconditioners for a kind of spatial fractional diffusion equations
- Numerical approximation to Prabhakar fractional Sturm-Liouville problem
- Finite difference/spectral approximations for the time-fractional diffusion equation
- Fast ADI method for high dimensional fractional diffusion equations in conservative form with preconditioned strategy
- A second-order accurate numerical approximation for the fractional diffusion equation
- Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in \(\mathbb R^2\)
- Finite difference methods for two-dimensional fractional dispersion equation
- Circulant-based approximate inverse preconditioners for a class of fractional diffusion equations
- A Proposal for Toeplitz Matrix Calculations
- Toeplitz Equations by Conjugate Gradients with Circulant Preconditioner
- Fast solution algorithms for exponentially tempered fractional diffusion equations
- On variational properties of balanced central fractional derivatives
- Fractional Differential Equations
- Preconditioning Techniques for Diagonal-times-Toeplitz Matrices in Fractional Diffusion Equations
- Crank--Nicolson Alternative Direction Implicit Method for Space-Fractional Diffusion Equations with Nonseparable Coefficients
- An Introduction to Iterative Toeplitz Solvers
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
