{"title":"Quasi‐Newton variable preconditioning for nonlinear elasticity systems in 3D","authors":"J. Karátson, S. Sysala, M. Béreš","doi":"10.1002/nla.2537","DOIUrl":null,"url":null,"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.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Linear Algebra with Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/nla.2537","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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