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

0579562 - ÚGN 2025 RIV US eng J - Journal Article
Karátson, J. - Sysala, Stanislav - Béreš, Michal
Quasi-Newton variable preconditioning for nonlinear elasticity systems in 3D.
Numerical Linear Algebra with Applications. Roč. 31, č. 3 (2024), č. článku e2537. ISSN 1070-5325. E-ISSN 1099-1506
Institutional support: RVO:68145535
Keywords : deflated conjugate gradient * mesh independence * nonlinear elasticity * preconditioning * Quasi-Newton methods
OECD category: Applied mathematics
Impact factor: 4.3, year: 2022
Method of publishing: Open access
https://onlinelibrary.wiley.com/doi/10.1002/nla.2537

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.
Permanent Link: https://hdl.handle.net/11104/0348374