A conforming auxiliary space preconditioner for the mass conserving stress-yielding method.

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2023-10-01 Epub Date: 2023-05-07 DOI:10.1002/nla.2503

Lukas Kogler, Philip L Lederer, Joachim Schöberl

引用次数: 0

Abstract

We are studying the efficient solution of the system of linear equations stemming from the mass conserving stress-yielding (MCS) discretization of the Stokes equations. We perform static condensation to arrive at a system for the pressure and velocity unknowns. An auxiliary space preconditioner for the positive definite velocity block makes use of efficient and scalable solvers for conforming Finite Element spaces of low order and is analyzed with emphasis placed on robustness in the polynomial degree of the discretization. Numerical experiments demonstrate the potential of this approach and the efficiency of the implementation.

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质量守恒应力屈服法的协调辅助空间预处理器

我们正在研究由Stokes方程的质量守恒应力屈服（MCS）离散化产生的线性方程组的有效解。我们进行静态冷凝，得到一个压力和速度未知的系统。正速度块的辅助空间预处理器利用高效和可扩展的求解器来协调低阶有限元空间，并对其进行了分析，重点是离散化多项式次数的鲁棒性。数值实验证明了这种方法的潜力和实现的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.