变系数反应扩散方程的双参数分裂预处理方法

蒋沁纱　陈浩

四川師范大学学报（自然科学版）第46卷第5期

摘要：考虑一类空间变系数反应扩散方程的快速算法.针对二阶改进道格拉斯分裂时间离散所得线性代数系统，构造一类双参数交替分裂迭代方法.分析格式的收敛性，给出最优参数的取值，并获得相应预处理子.数值结果验证新方法的有效性及相比单参数分裂迭代格式的优越性.

关键词：变系数反应扩散方程; 改进道格拉斯分裂方法; 双参数; 交替分裂迭代方法; 预处理子

中图分类号：O241.82; O241.6 文献标志码：A 文章编号：1001-8395（2023）05-0638-08

1离散

2交替分裂迭代算法

3数值实验

4结束语

本文考虑了变系数反应扩散方程的快速算法，针对改进道格拉斯分裂时间离散所得的线性代数系统，构造了一类双参数交替分裂迭代法，分析了其收敛性及最优参数的取值.同时，将其与GMRES结合，构造了一类预处理GMRES的方法，数值结果验证了新方法的收敛性.

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A Class of Alternating Splitting Preconditioning Method with Two Parameters

for Reaction-Diffusion Equations with Variable Coefficients in SpaceJIANG Qinsha，CHEN Hao（School of Mathematical Sciences， Chongqing Normal University， Chongqing 401331）

Abstract：This paper consider fast algorithms for solving a class of reaction-diffusion equations with variable coefficients. We propose an alternating splitting iterative method with two parameters for solving the linear algebraic systems resulting from the modified Douglas splitting discretization of the reaction-diffusion equations. We show that the proposed scheme is convergent and the optimal parameters are given. A splitting preconditioner is also derived for the linear system. Numerical results show that the proposed methods is effective and superior to the splitting iterative scheme with a single parameter.

Keywords：reaction-diffusion equation with variable coefficients; modified Douglas splitting method; two parameters; alternating splitting iteration method; preconditioner

2020 MSC：65F10; 65L06; 65N22

（編辑 余毅）