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Ordering Techniques for Two-and Three-Dimensional Convection-Dominated Elliqtic Boundary Value Problems

机译：对流和二维对流占主导的椭圆边值问题的排序技术

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Multigrid methods with simple smoothers have been proven to be very successful for elliptic problems with no or only moderate convection. In the predence of dominant convection or anisotropies as it mignht appear in equations of comprtational fluid dynamics (e.g.inthe Navier-Stokes equations), the convergence rate typically decreases. This is due to a weakened smoothing property as well as to problems on the coarse grib correction. In order to obtain a multigrid method that is robust for convection-dominated problems, we construct efficient smoothers that obtain their favorable properties through an appropriate ordering of the unknowns. We propose several ordering techniques that work on the graph associated with the (convective part of the )stiffness matrix. The ordering algorithms provide a numbering together with a block structure which can be used for block iterative metods. We provide numerical resuits for the Stokes equations with a convective term illustrating the improved convergence properties of the multigrid algorithm when applied with an appropriate ordering of the unknowns.
机译：已经证明，使用简单平滑器的多重网格方法对于没有对流或只有对流的椭圆问题非常成功。在显性对流或各向异性的存在下，它会出现在混合流体动力学方程（例如Navier-Stokes方程）中，收敛速度通常会降低。这是由于平滑性能减弱以及粗粒校正所引起的问题。为了获得对于对流占优的问题鲁棒的多网格方法，我们构造了有效的平滑器，该平滑器通过对未知数进行适当的排序来获得其有利的性能。我们提出了几种在与刚度矩阵的（对流部分）关联的图形上工作的排序技术。排序算法提供了编号以及可用于块迭代方法的块结构。我们使用对流项为Stokes方程提供数值结果，该对流项说明了在应用未知数的适当排序时多网格算法的改进的收敛性。

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