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首页> 外文期刊>International Journal for Multiscale Computational Engineering >Fast Deflation Methods with Applications to Two-Phase Flows
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Fast Deflation Methods with Applications to Two-Phase Flows

机译：快速放气方法及其在两相流中的应用

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摘要

Traditional Krylov iterative solvers, such as the preconditioned conjugate gradient method, can be accelerated by incorporating a second-level preconditioner. We use deflation as a second-level preconditioner, which is very efficient in many applications. In this paper, we give some theoretical results for the general deflation method applied to singular matrices, which provides us more insight into the properties and the behavior of the method. Moreover, we discuss stability issues of the deflation method and consider some ideas for a more stable method. In the numerical experiments, we apply the deflation method and its stabilized variant to singular linear systems derived from two-phase bubbly flow problems. Because of the appearance of bubbles, those linear systems are ill-conditioned, and therefore, they are usually hard to solve using traditional preconditioned Krylov iterative methods. We show that our deflation methods can be very efficient to solve the linear systems. Finally, we also investigate numerically the stability of these methods by examining the corresponding inner-outer iterations in more detail.
机译：传统的Krylov迭代求解器，例如预处理的共轭梯度法，可以通过合并第二级预处理器来加速。我们将放气用作第二级前提条件，这在许多应用中非常有效。在本文中，我们给出了适用于奇异矩阵的一般放气方法的一些理论结果，从而为我们提供了对该方法的性质和行为的更多了解。此外，我们讨论了放气方法的稳定性问题，并考虑了一些有关更稳定方法的想法。在数值实验中，我们将放气方法及其稳定的变型应用于源自两相气泡流问题的奇异线性系统。由于气泡的出现，这些线性系统是不良的，因此，通常很难使用传统的预处理Krylov迭代方法来求解。我们表明，我们的放气方法可以非常有效地解决线性系统。最后，我们还通过更详细地检查相应的内外迭代，从数值上研究了这些方法的稳定性。

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