Symbol-based preconditioning for Riesz distributed-order space-fractional diffusion equations

DOI10.1553/etna_vol54s499zbMath1501.65042OpenAlexW3190424693MaRDI QIDQ822685

N. E. Zubov

Publication date: 23 September 2021

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://etna.mcs.kent.edu/volumes/2021-2030/vol54/abstract.php?vol=54&pages=499-513

zbMATH Keywords

preconditioningspectral distributionToeplitz matricesfractional diffusion equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Fractional derivatives and integrals (26A33) Eigenvalues, singular values, and eigenvectors (15A18) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Finite difference methods for boundary value problems involving PDEs (65N06) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Toeplitz, Cauchy, and related matrices (15B05) Preconditioners for iterative methods (65F08) Fractional partial differential equations (35R11)

Related Items

On the extreme eigenvalues and asymptotic conditioning of a class of Toeplitz matrix-sequences arising from fractional problems, A note on the spectral analysis of matrix sequences via GLT momentary symbols: from all-at-once solution of parabolic problems to distributed fractional order matrices, Fine spectral estimates with applications to the optimally fast solution of large FDE linear systems, A class of preconditioner for solving the Riesz distributed-order nonlinear space-fractional diffusion equations

Cites Work

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• The Grünwald-Letnikov method for fractional differential equations
• A fourth-order approximation of fractional derivatives with its applications
• Spectral analysis and structure preserving preconditioners for fractional diffusion equations
• Fractional cable equation models for anomalous electrodiffusion in nerve cells: Infinite domain solutions
• The GLT class as a generalized Fourier analysis and applications
• On the condition numbers of large semi-definite Toeplitz matrices
• New PCG based algorithms for the solution of Hermitian Toeplitz systems
• On the extreme eigenvalues of Hermitian (block) Toeplitz matrices
• A numerical method for solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain
• Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations
• A novel finite volume method for the Riesz space distributed-order diffusion equation
• Error estimate of second-order finite difference scheme for solving the Riesz space distributed-order diffusion equation
• Waiting-times and returns in high-frequency financial data: An empirical study
• Finite difference/spectral-Galerkin method for a two-dimensional distributed-order time-space fractional reaction-diffusion equation
• An efficient finite volume method for nonlinear distributed-order space-fractional diffusion equations in three space dimensions
• Generalized Locally Toeplitz Sequences: Theory and Applications
• Non‐Hermitian perturbations of Hermitian matrix‐sequences and applications to the spectral analysis of the numerical approximation of partial differential equations
• Toeplitz Preconditioners Constructed from Linear Approximation Processes
• Spectral Analysis and Multigrid Methods for Finite Volume Approximations of Space-Fractional Diffusion Equations
• Any Circulant-Like Preconditioner for Multilevel Matrices Is Not Superlinear
• Generalized Locally Toeplitz Sequences: Theory and Applications