Analysis of some projection method based preconditioners for models of incompressible flow
Analysis of some projection method based preconditioners for models of incompressible flow
复制标题
不可压缩流动模型中基于投影法的预处理器分析
DOI：
10.1016/j.apnum.2014.12.003
复制
发表时间：
2013
影响因子：
2.8
通讯作者：
M. Cai
中科院分区：
文献类型：
--
作者：
M. Cai
本文研究了几种基于投影法的各种不可压缩流动模型的预处理器。在这些基于投影方法的预条件子的推导中，我们使用了三种不同类型的 Schur 补码的逆近似，即精确逆、Cahouet-Chabard 型近似和 BFBt 型近似。我们阐明了这些基于投影方法的预处理器和相关预处理器之间的联系和区别。对于使用 Cahouet-Chabard 型近似的预处理器，我们表明预处理系统的特征值具有与参数无关的统一界限，并且大多数等于 1。分析基于对换向差算子的详细讨论。此外，这些结果证明了交错网格离散化的稳定性并揭示了边界处理的效果。为了进一步说明这些基于投影方法的预处理器的有效性，给出了数值实验来将它们的性能与相关预处理器的性能进行比较。还讨论了基于投影方法的预处理器对其他鞍点问题的推广。
In this paper, several projection method based preconditioners for various incompressible flow models are studied. In the derivations of these projection method based preconditioners, we use three different types of the approximations of the inverse of the Schur complement, i.e., the exact inverse, the Cahouet–Chabard type approximation and the BFBt type approximation. We illuminate the connections and the distinctions between these projection method based preconditioners and those related preconditioners. For the preconditioners using the Cahouet–Chabard type approximation, we show that the eigenvalues of the preconditioned systems have uniform bounds independent of the parameters and most of them are equal to 1. The analysis is based on a detailed discussion of the commutator difference operator. Moreover, these results demonstrate the stability of the staggered grid discretization and reveal the effects of the boundary treatment. To further illustrate the effectiveness of these projection method based preconditioners, numerical experiments are given to compare their performances with those of the related preconditioners. Generalizations of the projection method based preconditioners to other saddle point problems are also discussed.