A Comparison of Deflation and Coarse Grid Correction Applied to Porous Media Flow
A Comparison of Deflation and Coarse Grid Correction Applied to Porous Media Flow
复制标题
多孔介质流的紧缩与粗网格校正的比较
DOI：
10.1137/s0036142903430451
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
C. Vuik
中科院分区：
文献类型：
--
作者：
R. Nabben;C. Vuik
本文比较了偏微分方程数值解的各种预条件子。我们比较了一个粗网格校正预处理区域分解方法与所谓的紧缩预处理。证明了对于所有的收缩向量和所有的约束条件，延迟预处理系统的有效条件数总是低于粗网格修正预处理系统的条件数.这意味着应用于延迟预处理系统的共轭梯度法总是比应用于粗网格校正预处理系统的共轭梯度法收敛得更快。多孔介质流动的数值结果强调了理论结果。
In this paper we compare various preconditioners for the numerical solution of partial dierential equations. We compare a coarse grid correction preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the de ated preconditioned system is always, i.e. for all deflation vectors and all restrictions and prolongations, below the condition number of the system preconditioned by the coarse grid correction. This implies that the Conjugate Gradient method applied to the de ated preconditioned system converges always faster than the Conjugate Gradient method applied to the system preconditioned by the coarse grid correction. Numerical results for porous media flows emphasize the theoretical results.