On the inexact symmetrized globally convergent semi-smooth Newton method for 3D contact problems with Tresca friction: the R-linear convergence rate. (2nd January 2020)

• Record Type: Journal Article
• Authors: Kučera, R.; Motyčková, K.; Markopoulos, A.; Haslinger, J.
• Is Part Of: Optimization methods and software. Volume 35:Number 1(2020)
• Page Start: 65
• Page End: 86
• Publication Date: 2020-01-02
• Subjects: Contact problem -- Tresca friction -- semi-smooth Newton method -- conjugate gradient method -- gradient projection -- convergence rate; 65K10 -- 65N22 -- 49M29 -- 74M15 -- 74M10; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1556659
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: The semi-smooth Newton method for solving discretized contact problems with Tresca friction in three-dimensional space is analysed. The slanting function is approximated to get symmetric inner linear systems. The primal–dual algorithm is transformed into the dual one so that the conjugate gradient method can be used. The R-linear convergence rate is proved for an inexact globally convergent variant of the method. Numerical experiments conclude the paper.