A PRECONDITIONED FAST HERMITE FINITE ELEMENT METHOD FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS

被引：12
|
作者：
Zhao, Meng [1 ]
Cheng, Aijie [1 ]
Wang, Hong [2 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
[2] Univ South Carolina, Dept Math, Columbia, SC 29208 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2017年 / 22卷 / 09期
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
Anomalous diffusion; space-fractional diffusion equation; hermite finite element; block Toeplitz matrix; fast Fourier transform; preconditioned conjugate gradient squared method; DIFFERENTIAL-EQUATIONS; DISPERSION EQUATIONS; ANOMALOUS DIFFUSION; TOEPLITZ-SYSTEMS; BOUNDED DOMAINS; GALERKIN METHOD; APPROXIMATIONS;
D O I：
10.3934/dcdsb.2017178
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We develop a fast Hermite finite element method for a one-dimensional space-fractional diffusion equation, by proving that the stiffness matrix of the method can be expressed as a Toeplitz block matrix. Then a block circulant preconditioner is presented. Numerical results are presented to show the utility of the fast method.
引用
收藏
页码：3529 / 3545
页数：17
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