二维椭圆方程边值问题拟多重网格预处理迭代法  

Quasi multigrid preconditioned iteration method for boundary value problem of two-dimensional elliptic equations

作　　者：白乙拉[1] 

机构地区：[1]渤海大学数理学院,辽宁锦州121013

出　　处：《渤海大学学报（自然科学版）》2012年第4期294-298,共5页Journal of Bohai University:Natural Science Edition

基　　金：大连理工大学海岸和近海工程国家重点实验室开放基金(No:LP1217)

摘　　要：针对二维椭圆型方程的数值求解问题,结合多重网格法和预处理方法的优点,构造出了一种求解二维椭圆型方程边值问题的迭代方法.数值结果表明,该方法能够有效地提高迭代法的收敛速度,迭代计算得到的数值解逼近精确解的精度高且稳定,较SOR方法有显著的优越性,是数值求解二维椭圆型方程边值问题的一种可靠、高效的方法.For numerical problem of two - dimensional elliptic equation, the paper combines the advantages of muhigrid method and preconditioned method, and constructs an iterative method for solving boundary value problem of two- dimensional elliptic equations. The numerical results show that this method can effectively im- prove the convergence rate of iteration method, the numerical solutions of iterative computation approach preci- sion of exact solution are higher and the numerical solutions are more stable, there are significant advantages compared to the SOR method, and it is a reliable and efficient method to solve boundary value problem of two - dimensional elliptic equations.

关 键 词：椭圆型方程 多重网格法 预处理 差分格式 

分 类 号：O241.8[理学—计算数学]