Quasi‐Newton variable preconditioning for nonlinear elasticity systems in 3D-Reference-Cited by-同舟云学术

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

Published:2023-10-23 Issue: Volume: Page:
ISSN:1070-5325
Container-title:Numerical Linear Algebra with Applications
language:en
Short-container-title:Numerical Linear Algebra App

Author:

Karátson J.¹²^ORCID,Sysala S.³^ORCID,Béreš M.³⁴^ORCID

Affiliation:

1. Department of Applied Analysis & ELKH‐ELTE Numerical Analysis and Large Networks Research Group Eötvös Loránd University Budapest Hungary

2. Department of Analysis and Operations Research Budapest University of Technology and Economics Budapest Hungary

3. Department of Applied Mathematics and Computer Science Institute of Geonics of the Czech Academy of Sciences Ostrava Czechia

4. Department of Applied Mathematics VSB–Technical University of Ostrava Ostrava Czechia

Abstract

SummaryQuasi‐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.

Publisher

Wiley

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/nla.2537

Reference28 articles.

1. BlahetaR.Multilevel Newton methods for nonlinear problems with applications to elasticity Copernicus 940820. Technical Report.

2. On a two-level Newton-type procedure applied for solving non-linear elasticity problems

3. Continuation Newton methods

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