A preconditioned fast finite volume method for two-dimensional conservative space-fractional diffusion equations on non-uniform meshes

被引：0

作者：

Xu, Yuan ^{[1
,2
]}

Lei, Siu-Long ^{[2
]}

Sun, Hai-Wei ^{[2
]}

Fang, Zhi-Wei ^{[3
]}

机构：

[1] Cent South Univ Forestry & Technol, Coll Comp & Math, Changsha 410004, Hunan, Peoples R China

[2] Univ Macau, Dept Math, Macau, Peoples R China

[3] Foshan Univ, Sch Math, Foshan 528000, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2025年 / 196卷

基金：

中国国家自然科学基金;

关键词：

Fractional diffusion equation; Non-uniform mesh; Sum-of-exponentials approximation; Preconditioned GMRES method; TIME-STEPPING METHOD; DIFFERENCE APPROXIMATIONS; OBLIVIOUS CONVOLUTION; ITERATIVE METHODS; DISPERSION; CONVERGENCE; STABILITY; SCHEME;

D O I：

10.1016/j.camwa.2025.07.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a finite volume (FV) method to solve two-dimensional (2D) conservative space-fractional diffusion equations (SFDEs) on non-uniform meshes via a sum-of-exponentials (SOE) technique. The SOE technique is used to approximate the spatial kernel, resulting in a numerically stable scheme. To further improve efficiency, a preconditioned fast Krylov subspace iterative method is exploited to obtain the numerical solution. The matrix-vector multiplication can be performed in (9(M log2 M) operations for a matrix of size M. Numerical experiments confirm the effectiveness of the proposed algorithm in terms of the computational time and the number of iterations.

引用

页码：30 / 48

页数：19

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