A dimension expanded preconditioning technique for block two-by-two linear equations

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2023-0260

Wei-Hua Luo, Bruno Carpentieri, Jun Guo

引用次数: 0

Abstract

Abstract In this article, we introduce a novel block preconditioner for block two-by-two linear equations by expanding the dimension of the coefficient matrix. Theoretical results on the eigenvalues distribution of the preconditioned matrix are obtained, and a feasible implementation is discussed. Some numerical examples, including the solution of the Navier-Stokes equations, are presented to support the theoretical findings and demonstrate the preconditioner’s efficiency.

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块二乘二线性方程的维数扩展预处理技术

摘要本文通过展开系数矩阵的维数，引入了一种新的块2乘2线性方程的块预条件。得到了预条件矩阵特征值分布的理论结果，并讨论了一种可行的实现方法。给出了一些数值例子，包括Navier-Stokes方程的解，以支持理论发现并证明了前置条件的有效性。

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

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.