A systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system
A systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system
复制标题
多孔弹性系统多重网格耦合平滑和分布平滑的系统比较
DOI：
10.1002/nla.372
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发表时间：
2004
影响因子：
4.3
通讯作者：
Roman Wienands
中科院分区：
文献类型：
--
作者：
F. Gaspar;F. Lisbona;C. Oosterlee;Roman Wienands
本文对交错网格上离散的多孔弹性方程组提出了一种有效的多重网格方法。特别是，我们从效率和稳健性两个方面比较了两种不同的平滑方法。一种方法是基于耦合松弛原理。我们介绍了耦合光滑器的“单元式”和“线式”版本。它们与分布松弛进行了比较，这给了我们一个解耦的方程系统。它可以用基本的迭代方法在方程上进行平滑。所有的平滑方法都被用于相同的孔弹性测试问题，其中的参数，如时间步长或LAMé系数是不同的。一些高效的方法得到了验证，数值实验证实了这一点。版权所有©2004 John Wiley&Sons，Ltd.
In this paper, we present efficient multigrid methods for the system of poroelasticity equations discretized on a staggered grid. In particular, we compare two different smoothing approaches with respect to efficiency and robustness. One approach is based on the coupled relaxation philosophy. We introduce ‘cell‐wise’ and ‘line‐wise’ versions of the coupled smoothers. They are compared with a distributive relaxation, that gives us a decoupled system of equations. It can be smoothed equation‐wise with basic iterative methods. All smoothing methods are evaluated for the same poroelasticity test problems in which parameters, like the time step, or the Lamé coefficients are varied. Some highly efficient methods result, as is confirmed by the numerical experiments. Copyright © 2004 John Wiley & Sons, Ltd.