Quasi‐Newton variable preconditioning for nonlinear elasticity systems in 3D

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2023-10-23 DOI:10.1002/nla.2537

J. Karátson, S. Sysala, M. Béreš

引用次数: 0

Abstract

Summary Quasi‐Newton iterations are constructed for the finite element solution of small‐strain nonlinear elasticity systems in 3D. The linearizations are based on spectral equivalence and hence considered as variable preconditioners arising from proper simplifications in the differential operator. Convergence is proved, providing bounds uniformly w.r.t. the FEM discretization. Convenient iterative solvers for linearized systems are also proposed. Numerical experiments in 3D confirm that the suggested quasi‐Newton methods are competitive with Newton's method.

查看原文本刊更多论文

三维非线性弹性系统的准牛顿变量预处理

摘要建立了三维小应变非线性弹性系统有限元解的准牛顿迭代。线性化是基于谱等价的，因此被认为是由微分算子的适当简化引起的变量前置条件。证明了该方法的收敛性，并在有限元离散化过程中给出了一致的边界。对线性化系统也提出了方便的迭代求解方法。三维数值实验证实了拟牛顿方法与牛顿方法的竞争。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.