求解热传导方程的二阶对角Runge-Kutta方法的时间并行预处理子  

A TIME-PARALLEL PRECONDITIONER FOR THE SECOND ORDER DIAGONAL RUNGE-KUTTA METHOD FOR SOLVING HEAT EQUATIONS

作　　者：谢银雯 张建华 XIE Yinwen;ZHANG Jianhua(School of Science,East China University of Technology,Nanchang,Jiangxi 330013,China)

机构地区：[1]东华理工大学理学院,江西南昌330013

出　　处：《井冈山大学学报（自然科学版）》2024年第6期8-16,共9页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(12061009);江西省自然科学基金项目(20202BAB201002)。

摘　　要：针对二阶对角Runge-Kutta方法离散二维热传导方程导出的all-at-once线性系统,本研究提出了一个高效α循环矩阵预处理子,证明了二阶对角Runge-Kutta方法的A稳定性,给出预处理矩阵向量乘积的快速计算步骤,并从理论上分析出迭代矩阵的谱上界具有与网格大小无关的收敛性质。最后数值实验证实了预处理子的有效性。For the all-at-once linear system derived from the second order diagonal Runge-Kutta discrete twodimensional heat equation,an efficientαcirculant preconditioner is proposed in this paper,and the A stability of the second order diagonal Runge-Kutta method is proved.Besides,the fast computation steps of the preconditioning matrix vector product are also given.The upper bound of the spectrum of the iterative matrix has the convergence property independent of the size of the grid.Finally,the effectiveness of the preconditioner is verified by numerical experiments.

关 键 词：热传导方程 RUNGE-KUTTA方法 α循环预处理子 GMRES方法 

分 类 号：O246[理学—计算数学]