多重网格法求解三维椭圆型偏微方程  

A Multi-grid Method for 3D Elliptic Partial Differential Equations

作　　者：魏永强[1] 陈辉[1] 罗志龙[1] 黄佳坤[1] 韩颖雯[1] 白瑞芳[1] 

机构地区：[1]东华理工大学,江西抚州344000

出　　处：《科技信息》2010年第11X期5-7,14,共4页Science & Technology Information

基　　金：江西省研究生创新专项资金自筹项目;东华理工大学研究生创新基金项目(YC08B030)支助

摘　　要：本文简要介绍了多重网格法的基本原理以及V、W循环方式的具体实现步骤。然后引用数值算例-三维椭圆型偏微分方程对其计算效果进行了分析,讨论了网格剖分数目对多重网格法的收敛速度和收敛精度的影响,得到其收敛速度与网格剖分数目无关,并有效地提高了有限差分计算的精度,充分地体现了多重网格法的高效性和收敛速度快等特点。此外,探讨了多重网格法各个部分的最优化组合,如V循环和W循环、前光滑和后光滑次数以及多重网格最大循环次数的最佳选取问题,对比分析了多重网格采用不同的循环方式和光滑次数下收敛精度和收敛速度的差异问题。This paper introduces the basic principles of multi-grid and the concrete process of V and W circle. Then a numerical exampleelliptic partial differential equations is cited, and its calculation effect is analyzed, discussed how does the number of mesh generation impact on the multi-grid convergence speed and convergence precision, the result shows that the convergence rate has nothing to do with the number of mesh generation, and could effectively improve the accuracy of the finite difference calculation, fully reflects the characteristics of high efficiency and fast convergence for the multi-grid method, etc. In addition, the paper discusses the optimal combination of various parts for multi-grid method, such as V cycle and W cycle, the number of pre-smoothing and post-smoothing, the maximum number of multi-grid cycle, compared different issues of convergence accuracy and convergence rate for using different mode of circulation and different number of smooth.

关 键 词：多重网格法 三维椭圆型偏微分方程 收敛速度 

分 类 号：O175.25[理学—数学]