Path-following and augmented Lagrangian methods for contact problems in linear elasticity

Research output: Contribution to journalArticle

Abstract

A certain regularization technique for contact problems leads to a family of problems that can be solved efficiently using infinite-dimensional semismooth Newton methods, or in this case equivalently, primal-dual active set strategies. We present two procedures that use a sequence of regularized problems to obtain the solution of the original contact problem: first-order augmented Lagrangian, and path-following methods. The first strategy is based on a multiplier-update, while path-following with respect to the regularization parameter uses theoretical results about the path-value function to increase the regularization parameter appropriately. Comprehensive numerical tests investigate the performance of the proposed strategies for both a 2D as well as a 3D contact problem.

Original languageEnglish (US)
Pages (from-to)533-547
Number of pages15
JournalJournal of Computational and Applied Mathematics
Volume203
Issue number2 SPEC. ISS.
DOIs
StatePublished - Jun 15 2007

Fingerprint

Augmented Lagrangian Method
Path Following
Linear Elasticity
Newton-Raphson method
Contact Problem
Contacts (fluid mechanics)
Elasticity
Regularization Parameter
Augmented Lagrangians
Active Set Strategy
Path-following Methods
Semismooth Newton Method
Augmented Lagrangian
Regularization Technique
Primal-dual
Value Function
Multiplier
Update
First-order
Path

Keywords

  • Active sets
  • Augmented Lagrangians
  • Contact problems
  • Path-following
  • Primal-dual methods
  • Semismooth Newton methods

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Path-following and augmented Lagrangian methods for contact problems in linear elasticity. / Stadler, Georg.

In: Journal of Computational and Applied Mathematics, Vol. 203, No. 2 SPEC. ISS., 15.06.2007, p. 533-547.

Research output: Contribution to journalArticle

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