變系數反應擴散方程的雙參數分裂預處理方法

蔣沁紗　陳浩

四川師范大學學報（自然科學版）第46卷第5期

摘要：考慮一類空間變系數反應擴散方程的快速算法.針對二階改進道格拉斯分裂時間離散所得線性代數系統，構造一類雙參數交替分裂迭代方法.分析格式的收斂性，給出最優參數的取值，并獲得相應預處理子.數值結果驗證新方法的有效性及相比單參數分裂迭代格式的優越性.

關鍵詞：變系數反應擴散方程; 改進道格拉斯分裂方法; 雙參數; 交替分裂迭代方法; 預處理子

中圖分類號：O241.82; O241.6 文獻標志碼：A 文章編號：1001-8395（2023）05-0638-08

1離散

2交替分裂迭代算法

3數值實驗

4結束語

本文考慮了變系數反應擴散方程的快速算法，針對改進道格拉斯分裂時間離散所得的線性代數系統，構造了一類雙參數交替分裂迭代法，分析了其收斂性及最優參數的取值.同時，將其與GMRES結合，構造了一類預處理GMRES的方法，數值結果驗證了新方法的收斂性.

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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

（編輯 余毅）