论文标题
stokes方程的非重叠块Smoother
Non-overlapping block smoothers for the Stokes equations
论文作者
论文摘要
重叠的块SmoOther有效地湿damp损失了多摩德方法中高度振荡组件的误差贡献，用于stokes方程，但计算上的误差量。本文集中于对在交错网格上离散的Stokes方程的新块Smoothers的开发和分析。这些Smoother是不重叠的，因此由于计算成本降低而需要理想。传统的几何多移民方法基于简单的点smohorth。但是，多族方法解决更困难的问题（例如Stokes方程）的效率导致计算上更昂贵的Smoother，例如重叠的块Smoothers。非重叠的Smoothers较便宜，但在文献中被认为效率较低。在本文中，我们开发了新的非重叠的Smoothers，即所谓的三合会Smoothers，并在Multigrid方法中展示了它们以求解Stokes方程的效率。此外，我们通过测量其计算成本并通过使用局部傅立叶分析来分析其行为来比较重叠和非重叠的smo夫。
Overlapping block smoothers efficiently damp the error contributions from highly oscillatory components within multigrid methods for the Stokes equations but they are computationally expensive. This paper is concentrated on the development and analysis of new block smoothers for the Stokes equations that are discretized on staggered grids. These smoothers are non-overlapping and therefore desirable due to reduced computational costs. Traditional geometric multigrid methods are based on simple pointwise smoothers. However, the efficiency of multigrid methods for solving more difficult problems such as the Stokes equations lead to computationally more expensive smoothers, e.g., overlapping block smoothers. Non-overlapping smoothers are less expensive, but have been considered less efficient in the literature. In this paper, we develop new non-overlapping smoothers, the so-called triad-wise smoothers, and show their efficiency within multigrid methods to solve the Stokes equations. In addition, we compare overlapping and non-overlapping smoothers by measuring their computational costs and analyzing their behavior by the use of local Fourier analysis.
