二维抛物型方程初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 parabolic equations

作　　者：杨艳南[1] 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）》2013年第3期250-255,共6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项目(No:LP1217)

摘　　要：将求解二维椭圆方程边值问题的拟多重网格预处理迭代法推广到二维抛物型方程中去,采用Crank-Nicolson格式来离散二维抛物型方程.由于网格节点顺序对迭代格式的构造至关重要,因此对每一时间层上的l层网格节点按照旋转红-黑序进行排序.数值试验表明,此方法迭代次数较SOR法有明显减少,迭代解与精确解的误差值相对较低,收敛速度较快.因此,在求解二维抛物型方程初边值问题中拟多重网格预处理迭代法是一种很有效的方法.The solution of quasi multigrid preconditioned iteration method for boundary value problem of two -dimensional elliptic equation is generalized to two- dimensional parabolic equation and uses Crank -Nicolson format to discrete two - dimensional parabolic equation. Because it is essential for the network nodes order to form the structure of the iterative format, the grid nodes of L layer in each time are sorted in sequence according to the rotating red -black order. The numerical experiment shows that the number of this kind of iterations re- duces more obviously than SOR method and the iterative solution and the exact solution bear the features with a relatively low error and a faster rate of convergence. Therefore, the quasi muhigrid preconditioned iteration meth- od for boundary value problem of two - dimensional parabolic equation is a very effective way to solve this prob- lem.

关 键 词：抛物型方程 预处理 多重网格法 差分格式 

分 类 号：O241.8[理学—计算数学]