A Preconditioned Fast Finite Volume Method for Distributed-Order Diffusion Equation and Applications

被引：4

作者：

Fu, Hongfei ^{[1
]}

Liu, Huan ^{[2
]}

Zheng, Xiangcheng ^{[3
]}

机构：

[1] China Univ Petr East China, Coll Sci, Qingdao 266580, Shandong, Peoples R China

[2] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

[3] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2019年 / 9卷 / 01期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Distributed-order diffusion equation; finite volume method; fast conjugate gradient method; circulant preconditioner; parameter identification; DIFFERENCE METHOD; CIRCULANT PRECONDITIONER; APPROXIMATIONS; SYSTEMS; SCHEME; MODEL;

D O I：

10.4208/eajam.160418.190518

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Crank-Nicolson finite volume scheme for the modeling of the Riesz space distributed-order diffusion equation is proposed. The corresponding linear system has a symmetric positive definite Toeplitz matrix. It can be efficiently stored in O(NK) memory. Moreover, for the finite volume scheme, a fast version of conjugate gradient (FCG) method is developed. Compared with the Gaussian elimination method, the computational complexity is reduced from O(MN3 + NK) to O(l(A) MN logN + NK), where l(A) is the average number of iterations at a time level. Further reduction of the computational cost is achieved due to use of a circulant preconditioner. The preconditioned fast finite volume method is combined with the Levenberg-Marquardt method to identify the free parameters of a distribution function. Numerical experiments show the efficiency of the method.

引用

页码：28 / 44

页数：17

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