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 3 2区 数学 Q1 MATHEMATICS, APPLIED
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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
CiteScore
5.50
自引率
3.20%
发文量
209
审稿时长
1 months
期刊介绍: The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems. SISC papers are classified into three categories: 1. Methods and Algorithms for Scientific Computing: Papers in this category may include theoretical analysis, provided that the relevance to applications in science and engineering is demonstrated. They should contain meaningful computational results and theoretical results or strong heuristics supporting the performance of new algorithms. 2. Computational Methods in Science and Engineering: Papers in this section will typically describe novel methodologies for solving a specific problem in computational science or engineering. They should contain enough information about the application to orient other computational scientists but should omit details of interest mainly to the applications specialist. 3. Software and High-Performance Computing: Papers in this category should concern the novel design and development of computational methods and high-quality software, parallel algorithms, high-performance computing issues, new architectures, data analysis, or visualization. The primary focus should be on computational methods that have potentially large impact for an important class of scientific or engineering problems.
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