论文标题
最佳平滑因子，用于MAC方案的MAC方案三个，三个。
Optimal smoothing factor with coarsening by three for the MAC scheme for the Stokes equations
论文作者
论文摘要
在这项工作中，我们提出了一种用于多机方法的局部傅立叶分析，用于将其用于stokes方程的交错有限差分方法的变形为三倍。在[21]中，局部傅立叶分析已应用于基于质量的盲目 - 撒拉嗪松弛，一种基于质量的$σ$ -Uzawa松弛和基于质量的分布放松，并在Stokes方程式交错的网格上进行标准块。在这里，我们考虑了这些放松方案的多移民方法，并通过三个方法进行粗化。我们为这种粗化策略提供理论上最佳的平滑因子。浓缩三个的最佳平滑因子几乎等于从标准块中获得的最佳平滑因子。因此，在计算上进行的三个是优越的。此外，由三个块状产生了一个嵌套的网格层次结构，该网格简化并统一了网格转移操作员的构建。
In this work, we propose a local Fourier analysis for multigrid methods with coarsening by a factor of three for the staggered finite-difference method applied to the Stokes equations. In [21], local Fourier analysis has been applied to a mass-based Braess-Sarazin relaxation, a mass-based $σ$-Uzawa relaxation, and a mass-based distributive relaxation, with standard coarsening on staggered grids for the Stokes equations. Here, we consider multigrid methods with coarsening by three for these relaxation schemes. We derive theoretically optimal smoothing factors for this coarsening strategy. The optimal smoothing factors of coarsening by three are nearly equal to those obtained from standard coarsening. Thus, coarsening by three is superior computationally. Moreover, coarsening by three generates a nested hierarchy of grids, which simplifies and unifies the construction of grid-transfer operators.
