A Multigrid Method for Nonlocal Problems: Non--Diagonally Dominant or Toeplitz-Plus-Tridiagonal Systems
DOI10.1137/18M1210460zbMath1461.65236arXiv1808.09595OpenAlexW3091806392MaRDI QIDQ5146621
Stefano Serra Capizzano, Minghua Chen, Sven-Erik Ekström
Publication date: 26 January 2021
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1808.09595
fast Fourier transformmultigrid methodsnonlocal problemsnon-diagonally dominant systemToeplitz-plus-tridiagonal system
Fractional derivatives and integrals (26A33) Numerical methods for discrete and fast Fourier transforms (65T50) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Direct numerical methods for linear systems and matrix inversion (65F05) Toeplitz, Cauchy, and related matrices (15B05) Fractional partial differential equations (35R11)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
- Analysis of a scalar nonlocal peridynamic model with a sign changing kernel
- Multigrid method for fractional diffusion equations
- Second-order LOD multigrid method for multidimensional Riesz fractional diffusion equation
- Ten equivalent definitions of the fractional Laplace operator
- A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model
- Spectral analysis and structure preserving preconditioners for fractional diffusion equations
- A \(V\)-cycle multigrid for multilevel matrix algebras: proof of optimality
- On the extreme eigenvalues of Hermitian (block) Toeplitz matrices
- Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations
- Uniform convergence of V-cycle multigrid algorithms for two-dimensional fractional Feynman-Kac equation
- Convergence analysis of two-grid methods for elliptic Toeplitz and PDEs matrix-sequences
- On the extreme spectral properties of Toeplitz matrices generated by \(L^ 1\) functions with several minima/maxima
- Reformulation of elasticity theory for discontinuities and long-range forces
- Two-grid methods for Hermitian positive definite linear systems connected with an order relation
- Uniform convergence of V-cycle multigrid finite element method for one-dimensional time-dependent fractional problem
- Generalized grid transfer operators for multigrid methods applied on Toeplitz matrices
- Multigrid methods for space fractional partial differential equations
- A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
- Convergence Estimates for Multigrid Algorithms without Regularity Assumptions
- Numerical behaviour of multigrid methods for symmetric Sinc–Galerkin systems
- Sharp Estimates for Multigrid Rates of Convergence with General Smoothing and Acceleration
- New Convergence Estimates for Multigrid Algorithms
- Multigrid Method for Ill-Conditioned Symmetric Toeplitz Systems
- A Multigrid Tutorial, Second Edition
- A Riesz Basis Galerkin Method for the Tempered Fractional Laplacian
- Algebraic multigrid methods
- V-cycle Optimal Convergence for Certain (Multilevel) Structured Linear Systems
- Multigrid Methods for Symmetric Positive Definite Block Toeplitz Matrices with Nonnegative Generating Functions
- Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
- Preconditioning Techniques for Diagonal-times-Toeplitz Matrices in Fractional Diffusion Equations
- Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach
- High Order Algorithms for the Fractional Substantial Diffusion Equation with Truncated Lévy Flights
- Convergence Analysis of a Multigrid Method for a Nonlocal Model
- Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations
- An Introduction to Iterative Toeplitz Solvers
- Conditioning Analysis of Nonlocal Integral Operators in Fractional Sobolev Spaces
- Multilevel methods for nonuniformly elliptic operators and fractional diffusion
- A review of algebraic multigrid
