变系数反应扩散方程的双参数分裂预处理方法

A Class of Alternating Splitting Preconditioning Method with Two Parameters for Reaction-Diffusion Equations with Variable Coefficients in Space

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.

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.