Superlinear Krylov convergence under streamline diffusion FEM for convection‐dominated elliptic operators

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2024-09-02 DOI:10.1002/nla.2586

János Karátson

引用次数: 0

Abstract

This paper studies the superlinear convergence of Krylov iterations under the streamline‐diffusion preconditioning operator for convection‐dominated elliptic problems. First, convergence results are given involving the diffusion parameter . Then the limiting case is studied on the operator level, and the convergence results are extended to this situation under some conditions, in spite of the lack of compactness of the perturbation operators. An explicit rate is also given.

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对流主导椭圆算子流线扩散有限元下的超线性克雷洛夫收敛

本文研究了对流主导椭圆问题的流线-扩散预处理算子下 Krylov 迭代的超线性收敛性。首先，给出了涉及扩散参数 .然后，在算子层面研究了极限情况，并在某些条件下将收敛结果扩展到这种情况，尽管扰动算子缺乏紧凑性。此外，还给出了显式速率。

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.