A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes

DOI10.1016/j.camwa.2022.01.015OpenAlexW4205108995MaRDI QIDQ2074117

Zhi-Wei Fang, Hai-Wei Sun, Jia-li Zhang

Publication date: 4 February 2022

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2022.01.015

zbMATH Keywords

finite volume methodfast algorithmbanded preconditionerspatial fractional diffusion equationssum-of-exponentials technique

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) 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) Fractional partial differential equations (35R11) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (4)

Novel adaptive finite volume method on unstructured meshes for time-domain wave scattering and diffraction ⋮ Numerical calculation and fast method for the magnetohydrodynamic flow and heat transfer of fractional Jeffrey fluid on a two-dimensional irregular convex domain ⋮ An efficient conservative splitting characteristic difference method for solving 2-d space-fractional advection-diffusion equations ⋮ An efficient multigrid method with preconditioned smoother for two-dimensional anisotropic space-fractional diffusion equations

Cites Work

• Unnamed Item
• Unnamed Item
• Fast finite volume methods for space-fractional diffusion equations
• A circulant preconditioner for fractional diffusion equations
• Multigrid method for fractional diffusion equations
• Fast preconditioned iterative methods for finite volume discretization of steady-state space-fractional diffusion equations
• An \(O(N \log ^{2}N)\) alternating-direction finite difference method for two-dimensional fractional diffusion equations
• A preconditioned fast finite volume scheme for a fractional differential equation discretized on a locally refined composite mesh
• Numerical simulation for conservative fractional diffusion equations by an expanded mixed formulation
• A stable fast time-stepping method for fractional integral and derivative operators
• A finite volume method for two-sided fractional diffusion equations on non-uniform meshes
• A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations
• A fast finite volume method for conservative space-time fractional diffusion equations discretized on space-time locally refined meshes
• Stability and convergence of a Crank-Nicolson finite volume method for space fractional diffusion equations
• A Kernel Compression Scheme for Fractional Differential Equations
• A Fast Time Stepping Method for Evaluating Fractional Integrals
• Adaptive, Fast, and Oblivious Convolution in Evolution Equations with Memory
• Fast Convolution for Nonreflecting Boundary Conditions
• Fast Summation by Interval Clustering for an Evolution Equation with Memory
• A Fast Algorithm for the Caputo Fractional Derivative
• An approximate inverse preconditioner for spatial fractional diffusion equations with piecewise continuous coefficients
• An efficient positive‐definite block‐preconditioned finite volume solver for two‐sided fractional diffusion equations on composite mesh
• Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
• Preconditioning Techniques for Diagonal-times-Toeplitz Matrices in Fractional Diffusion Equations
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Fast and Oblivious Convolution Quadrature
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

This page was built for publication: A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes