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

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Keywords

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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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