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代数多重网格入门 03 粗网格矫正以及多重网格结构

代数多重网格入门 03 粗网格矫正以及多重网格结构

代数多重网格入门 03 粗网格矫正以及多重网格结构
第三部分: 粗网格矫正以及多层网格结构 代数多重网格(AMG)是利用几何多重网格(Geometric Multigrid, GMG)的一些重要原则和理念发展起来的不依赖于实际几何网格的多重网格方法。它继承了几何多重网格的主要优点,并且可以被用于更多类型的线性方程组。AMG 不依赖于任何实际几何网格信息,通过矩阵来定义粗网格和构造粗矩阵。迭代模式是从最细网格开始不断粗化、前平滑、粗化……到最粗网格,然后不断插值、后平滑、插值……回到最细网格。这样的一个循环称为V-循环(V-Cycle)。多重网格的迭代模式还有W-循环,完全多重网格(full multigrid, FMG, 也叫F-循环)等。

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