论文标题
无基质的单片多移民方法用于Stokes和广义stokes问题
Matrix-free Monolithic Multigrid Methods for Stokes and Generalized Stokes Problems
论文作者
论文摘要
我们考虑了广泛使用的连续$ \ MATHCAL {Q} _ {k} $ - $ \ MATHCAL {Q} _ {k-1} $ quadrililallal或hexahedral-hood-hood-hood元素，用于在两个和三个Spatial dimensions中的Stokes和Permialized Stokes Systems的有限元元素。对于相应的对称元素方程的相应对称但不确定系统的快速解决方案，我们建议和分析基于适当缩放的Chebyshev-Jacobi Smoothers的无基质整体几何多物种求解器。该分析基于Schöberl和Zulehner（2003）的结果。我们介绍并讨论了典型基准问题的几个数值结果。
We consider the widely used continuous $\mathcal{Q}_{k}$-$\mathcal{Q}_{k-1}$ quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions. For the fast solution of the corresponding symmetric, but indefinite system of finite element equations, we propose and analyze matrix-free monolithic geometric multigrid solvers that are based on appropriately scaled Chebyshev-Jacobi smoothers. The analysis is based on results by Schöberl and Zulehner (2003). We present and discuss several numerical results for typical benchmark problems.
