关于非局部扩散模型的一种快速预处理算法  

A Fast Preconditioned Algorithm for Nonlocal Diffusion Model

作　　者：冉育红 李存吉 殷俊锋[2] RAN Yuhong;LI Cunji;YIN Junfeng(School of Mathematics,Northwest University,Xi’an 710127,China;School of Mathematics,Tongji University,Shanghai 200092,China)

机构地区：[1]西北大学数学学院,陕西西安710127 [2]同济大学数学学院,上海200092

出　　处：《同济大学学报（自然科学版）》2021年第4期569-576,共8页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金面上项目(11971354)。

摘　　要：变系数非局部扩散模型可以被一种快速配置法进行有效的数值离散。离散后得到一个系数矩阵具有Toeplitz结构且稠密的线性方程组。由于系数矩阵是非对称的,该线性方程组可以用广义极小残量法(GMRES)方法求解。为了提高GMRES方法的收敛率,构造了系数矩阵的Toeplitz及循环预处理子,并提出了预处理GMRES方法求解该线性方程组。数值算例也表明了该预处理算法的有效性。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.

关 键 词：非局部扩散模型 快速配置法 TOEPLITZ矩阵 预处理 GMRES方法 

分 类 号：O241.6[理学—计算数学]