A Fast Preconditioned Algorithm for Nonlocal Diffusion Model

被引：0
|
作者：
Ran Y. [1 ,2 ]
Li C. [1 ,2 ]
Yin J. [3 ]
机构：
[1] School of Mathematics, Northwest University, Xi'an
[2] School of Mathematics, Northwest University, Xi'an
[3] School of Mathematics, Tongji University, Shanghai
来源：
Tongji Daxue Xuebao/Journal of Tongji University | 2021年 / 49卷 / 04期
关键词：
Collocation method; Generalized minimum residual method; Nonlocal diffusion model; Preconditioning; Toeplitz matrix;
D O I：
10.11908/j.issn.0253-374x.20308
中图分类号：
学科分类号：
摘要：
A fast collocation scheme can be used to discretize the variable-coefficient nonlocal diffusion model effectively. The coefficient matrix of the resulting linear system is unsymmetrical, dense and Toeplitz-like. The generalized minimum residual (GMRES) method can be employed to solve the discretized linear systems. In order to improve the rate of convergence of the GMRES method, the Toeplitz preconditioner and circulant preconditioner are constructed for the coefficient matrix, and the preconditioned GMRES methods are proposed for solving the discretized linear systems. Numerical examples are presented to illustrate the effectiveness of the preconditioned methods. © 2021, Editorial Department of Journal of Tongji University. All right reserved.
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页码：569 / 576
页数：7
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