DOI10.1016/j.jcp.2011.10.005zbMath1243.65117OpenAlexW1999695483MaRDI QIDQ419007
Hong-Kui Pang, Hai-Wei Sun
Publication date: 30 May 2012
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2011.10.005
A GPIU method for fractional diffusion equations,
The Hamiltonian structure and fast energy-preserving algorithms for the fractional Klein-Gordon equation,
A preconditioned fast Hermite finite element method for space-fractional diffusion equations,
Block splitting preconditioner for time-space fractional diffusion equations,
Fast numerical contour integral method for fractional diffusion equations,
Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations,
Stability and convergence of the Crank-Nicolson scheme for a class of variable-coefficient tempered fractional diffusion equations,
A framework of the harmonic Arnoldi method for evaluating \(\varphi\)-functions with applications to exponential integrators,
High order schemes for the tempered fractional diffusion equations,
A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients,
Second-order explicit difference schemes for the space fractional advection diffusion equation,
Multigrid methods for space fractional partial differential equations,
A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations,
Gaussian radial basis function and quadrature sinc method for two-dimensional space-fractional diffusion equations,
Stability and convergence of a Crank-Nicolson finite volume method for space fractional diffusion equations,
A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation,
Numerical and analytical solutions of new generalized fractional diffusion equation,
A Kronecker product splitting preconditioner for two-dimensional space-fractional diffusion equations,
Numerical simulation for 2D/3D time fractional Maxwell's system based on a fast second-order FDTD algorithm,
Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners,
Preconditioned iterative methods for fractional diffusion equation,
Fast alternating-direction finite difference methods for three-dimensional space-fractional diffusion equations,
An explicit high order method for fractional advection diffusion equations,
On CSCS-based iteration method for tempered fractional diffusion equations,
Fast ADI method for high dimensional fractional diffusion equations in conservative form with preconditioned strategy,
Numerical approaches to the functional distribution of anomalous diffusion with both traps and flights,
Computational challenge of fractional differential equations and the potential solutions: a survey,
Finite element multigrid method for the boundary value problem of fractional advection dispersion equation,
Circulant-based approximate inverse preconditioners for a class of fractional diffusion equations,
A fast preconditioned policy iteration method for solving the tempered fractional HJB equation governing American options valuation,
High order algorithm for the time-tempered fractional Feynman-Kac equation,
Efficient preconditioners for Radau-IIA time discretization of space fractional diffusion equations,
Preconditioning for symmetric positive definite systems in balanced fractional diffusion equations,
A Legendre spectral method on graded meshes for the two-dimensional multi-term time-fractional diffusion equation with non-smooth solutions,
Fast solvers for finite difference scheme of two-dimensional time-space fractional differential equations,
Preconditioned quasi-compact boundary value methods for space-fractional diffusion equations,
An improved algorithm based on finite difference schemes for fractional boundary value problems with nonsmooth solution,
A multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations,
Fourth order compact scheme for space fractional advection-diffusion reaction equations with variable coefficients,
A circulant preconditioner for fractional diffusion equations,
Least-squared mixed variational formulation based on space decomposition for a kind of variable-coefficient fractional diffusion problems,
Multigrid preconditioners for anisotropic space-fractional diffusion equations,
An implicit difference scheme with the KPS preconditioner for two-dimensional time-space fractional convection-diffusion equations,
A fast \(O(N\log N)\) finite difference method for the one-dimensional space-fractional diffusion equation,
Fractional Laplace operator in two dimensions, approximating matrices, and related spectral analysis,
Domain decomposition methods for space fractional partial differential equations,
Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations,
An efficient iteration method for Toeplitz-plus-band triangular systems generated from fractional ordinary differential equation,
Strang-type preconditioners for solving fractional diffusion equations by boundary value methods,
Second-order LOD multigrid method for multidimensional Riesz fractional diffusion equation,
Fast matrix splitting preconditioners for higher dimensional spatial fractional diffusion equations,
Fast spectral Petrov-Galerkin method for fractional elliptic equations,
Fourier spectral methods for fractional-in-space reaction-diffusion equations,
Numerical schemes of the time tempered fractional Feynman-Kac equation,
A divide-and-conquer fast finite difference method for space-time fractional partial differential equation,
Linearized difference schemes for a BBM equation with a fractional nonlocal viscous term,
Uniform convergence of V-cycle multigrid algorithms for two-dimensional fractional Feynman-Kac equation,
Fast preconditioned iterative methods for finite volume discretization of steady-state space-fractional diffusion equations,
All-at-once multigrid approaches for one-dimensional space-fractional diffusion equations,
Fast direct solver for CN-ADI-FV scheme to two-dimensional Riesz space-fractional diffusion equations,
An efficient multigrid solver for two-dimensional spatial fractional diffusion equations with variable coefficients,
Solvability and approximation of two-side conservative fractional diffusion problems with variable-coefficient based on least-squares,
Estimation of a permeability field within the two-phase porous media flow using nonlinear multigrid method,
A banded preconditioning iteration method for time-space fractional advection-diffusion equations,
PCG method with Strang's circulant preconditioner for Hermitian positive definite linear system in Riesz space fractional advection-dispersion equations,
Dominant Hermitian splitting iteration method for discrete space-fractional diffusion equations,
Kronecker product based preconditioners for boundary value method discretizations of space fractional diffusion equations,
Parallel-in-time multigrid for space-time finite element approximations of two-dimensional space-fractional diffusion equations,
Fourth order finite difference schemes for time-space fractional sub-diffusion equations,
A note on the stability of a second order finite difference scheme for space fractional diffusion equations,
Circulant preconditioners for a kind of spatial fractional diffusion equations,
Uniform convergence of V-cycle multigrid finite element method for one-dimensional time-dependent fractional problem,
Banded preconditioners for Riesz space fractional diffusion equations,
Preconditioned iterative methods for space-time fractional advection-diffusion equations,
A fourth-order approximation of fractional derivatives with its applications,
A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices,
Fast numerical solution for fractional diffusion equations by exponential quadrature rule,
Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients,
Spectral analysis and structure preserving preconditioners for fractional diffusion equations,
An analysis of a second order difference scheme for the fractional subdiffusion system,
Superconvergence points for the spectral interpolation of Riesz fractional derivatives,
A preconditioner based on sine transform for two-dimensional semi-linear Riesz space fractional diffusion equations in convex domains,
A spatial fourth-order maximum principle preserving operator splitting scheme for the multi-dimensional fractional Allen-Cahn equation,
Numerical solution for multi-dimensional Riesz fractional nonlinear reaction-diffusion equation by exponential Runge-Kutta method,
Adaptive finite element method for fractional differential equations using hierarchical matrices,
A fast explicit diffusion algorithm of fractional order anisotropic diffusion for image denoising,
A limited-memory block bi-diagonal Toeplitz preconditioner for block lower triangular Toeplitz system from time-space fractional diffusion equation,
The accuracy and stability of CN-WSGD schemes for space fractional diffusion equation,
A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes,
On \(\tau\) matrix-based approximate inverse preconditioning technique for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equations,
Fast and high-order accuracy numerical methods for time-dependent nonlocal problems in \(\mathbb{R}^2\),
An unconditionally convergent RSCSCS iteration method for Riesz space fractional diffusion equations with variable coefficients,
An efficient multigrid method with preconditioned smoother for two-dimensional anisotropic space-fractional diffusion equations,
Tensor-train format solution with preconditioned iterative method for high dimensional time-dependent space-fractional diffusion equations with error analysis,
A fast second-order implicit scheme for non-linear time-space fractional diffusion equation with time delay and drift term,
Block preconditioning strategies for time-space fractional diffusion equations,
A parallel algorithm for the Riesz fractional reaction-diffusion equation with explicit finite difference method,
Fast finite volume methods for space-fractional diffusion equations,
A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equations,
Incomplete circulant and skew-circulant splitting iteration method for time-dependent space fractional diffusion equations,
A circulant preconditioner for the Riesz distributed-order space-fractional diffusion equations,
Spectral Analysis and Multigrid Methods for Finite Volume Approximations of Space-Fractional Diffusion Equations,
Circulant and skew-circulant splitting iteration for fractional advection–diffusion equations,
Multigrid Waveform Relaxation for the Time-Fractional Heat Equation,
A fast preconditioning iterative method for solving the discretized second-order space-fractional advection-diffusion equations,
A \(\tau \)-preconditioner for a non-symmetric linear system arising from multi-dimensional Riemann-Liouville fractional diffusion equation,
Convergence analysis of a fast second‐order time‐stepping numerical method for two‐dimensional nonlinear time–space fractional Schrödinger equation,
Numerical study of a fast two-level Strang splitting method for spatial fractional Allen-Cahn equations,
Fast TTTS iteration methods for implicit Runge-Kutta temporal discretization of Riesz space fractional advection-diffusion equations,
An efficient fourth-order accurate conservative scheme for Riesz space fractional Schrödinger equation with wave operator,
A rational preconditioner for multi-dimensional Riesz fractional diffusion equations,
A Simple Solver for the Fractional Laplacian in Multiple Dimensions,
A Fast Two-Level Strang Splitting Method for Multi-Dimensional Spatial Fractional Allen-Cahn Equations with Discrete Maximum Principle,
Convergence Analysis of a Multigrid Method for a Nonlocal Model,
A Grid-Overlay Finite Difference Method for the Fractional Laplacian on Arbitrary Bounded Domains,
Exploiting multilevel Toeplitz structures in high dimensional nonlocal diffusion,
On \(\tau\)-preconditioner for a novel fourth-order difference scheme of two-dimensional Riesz space-fractional diffusion equations,
Banded $M$-Matrix Splitting Preconditioner for Riesz Space Fractional Reaction-Dispersion Equation,
Fast solution methods for Riesz space fractional diffusion equations with non-separable coefficients,
Multilevel Circulant Preconditioner for High-Dimensional Fractional Diffusion Equations,
A Multigrid Method for Nonlocal Problems: Non--Diagonally Dominant or Toeplitz-Plus-Tridiagonal Systems,
A New Family of Difference Schemes for Space Fractional Advection Diffusion Equation,
Fully Finite Element Adaptive AMG Method for Time-Space Caputo-Riesz Fractional Diffusion Equations,
Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations,
Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme,
A Eulerian–Lagrangian control volume method for solute transport with anomalous diffusion,
Fast Iterative Solvers for Linear Systems Arising from Time-Dependent Space-Fractional Diffusion Equations,
Fast algorithms for high-order numerical methods for space-fractional diffusion equations,
A posteriori error analysis for a fractional differential equation,
Superconvergence points of integer and fractional derivatives of special Hermite interpolations and its applications in solving FDEs,
Fast Solvers for Two-Dimensional Fractional Diffusion Equations Using Rank Structured Matrices,
Preconditioners for Symmetrized Toeplitz and Multilevel Toeplitz Matrices,
Crank--Nicolson Alternative Direction Implicit Method for Space-Fractional Diffusion Equations with Nonseparable Coefficients,
Solving fractional diffusion equations by Sinc and radial basis functions,
High Order Algorithms for the Fractional Substantial Diffusion Equation with Truncated Lévy Flights,
A Splitting Preconditioner for Toeplitz-Like Linear Systems Arising from Fractional Diffusion Equations,
On circulant and skew-circulant preconditioned Krylov methods for steady-state Riesz spatial fractional diffusion equations,
Numerical methods for fractional partial differential equations,
Efficient Legendre spectral tau algorithm for solving the two-sided space–time Caputo fractional advection–dispersion equation,
An approximate inverse preconditioner for spatial fractional diffusion equations with piecewise continuous coefficients,
Kronecker product-based structure preserving preconditioner for three-dimensional space-fractional diffusion equations