斯托克斯和广义斯托克斯问题的无矩阵整体多网格方法

IF 4.3 3区材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

ACS Applied Electronic Materials Pub Date : 2024-05-09 DOI:10.1137/22m1504184

Daniel Jodlbauer, Ulrich Langer, Thomas Wick, Walter Zulehner

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引用次数: 0

摘要

SIAM 科学计算期刊》，第 46 卷第 3 期，第 A1599-A1627 页，2024 年 6 月。摘要。我们考虑将广泛使用的连续[math]-[math]四边形或六面体 Taylor-Hood 元素用于二维和三维斯托克斯和广义斯托克斯系统的有限元离散化。为了快速求解相应的对称但不确定的有限元方程组，我们提出并分析了基于适当比例的切比雪夫-雅可比平滑器的无矩阵单片几何多网格求解器。分析以 Schöberl 和 Zulehner (2003) 的结果为基础。我们介绍并讨论了几个典型基准问题的数值结果。

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Matrix-Free Monolithic Multigrid Methods for Stokes and Generalized Stokes Problems

SIAM Journal on Scientific Computing, Volume 46, Issue 3, Page A1599-A1627, June 2024.
Abstract. We consider the widely used continuous [math]-[math] 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.

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来源期刊

ACS Applied Electronic Materials Multiple-

CiteScore

7.20

自引率

4.30%

发文量

567