基于SOR多重网格迭代法的最优解研究  

Research on Optimal Solution Based on SOR Multigrid Iteration Method

作　　者：邵迟 周斌[1] 张超[1] 

机构地区：[1]湖南工业大学土木工程学院,湖南株洲412007

出　　处：《太原师范学院学报（自然科学版）》2017年第1期30-33,41,共5页Journal of Taiyuan Normal University:Natural Science Edition

摘　　要：为寻求一种高速运行的迭代方法获得最优解,基于传统的SOR迭代法,建立两层区域中心模式网格模型,引入两个最基本的偏微分方程算例,给定边界条件与终止条件,利用Matlab多次迭代算法模拟谱半径与最优解的关系图、迭代次数与最优解的关系图,对提出的校正公式进行验证,结果表明:校正公式计算的结果与数值模拟的结果非常接近,且存在一最优解,随着谱半径、迭代次数的增加,最优解的迭代效率呈对数增加.In order to seek a high-speed operation of the iterative method to obtain optimal solution, SOR iterative method based on the traditional established two grid model of regional center model, introducing two basic examples of partial differential equations, and the termina- tion condition of the given boundary conditions, using Matlab iteration algorithm simulation dia- gram diagram, the number of iterations and the optimal solution the spectral radius and the opti- mal solution is verified on the correction formula is put forward. The results showed that the cor- rection formula of calculation results and numerical simulation results are very close, and there is an optimal solution, with the increase of spectral radius, the number of iterations, the iterative efficiency of the optimal solution shows a logarithmic increase.

关 键 词：最优解 SOR法 网格模型 谱半径 迭代次数 

分 类 号：O302[理学—力学]