A primal-dual active set algorithm for three-dimensional contact problems with Coulomb friction

S. Hüeber, Georg Stadler, B. I. Wohlmuth

Research output: Contribution to journalArticle

Abstract

In this paper, efficient algorithms for contact problems with Tresca and Coulomb friction in three dimensions are presented and analyzed. The numerical approximation is based on mortar methods for nonconforming meshes with dual Lagrange multipliers. Using a nonsmooth complementarity function for the three-dimensional friction conditions, a primal-dual active set algorithm is derived. The method determines active contact and friction nodes and, at the same time, resolves the additional nonlinearity originating from sliding nodes. No regularization and no penalization are applied, and superlinear convergence can be observed locally. In combination with a multigrid method, it defines a robust and fast strategy for contact problems with Tresca or Coulomb friction. The efficiency and flexibility of the method is illustrated by several numerical examples.

Original languageEnglish (US)
Pages (from-to)572-596
Number of pages25
JournalSIAM Journal on Scientific Computing
Volume30
Issue number2
DOIs
StatePublished - 2007

Fingerprint

Active Set
Coulomb Friction
Primal-dual
Contact Problem
Friction
Mortar Method
Three-dimensional
Superlinear Convergence
Penalization
Multigrid Method
Complementarity
Vertex of a graph
Lagrange multipliers
Numerical Approximation
Three-dimension
Resolve
Regularization
Efficient Algorithms
Flexibility
Mesh

Keywords

  • 3D Coulomb friction
  • Contact problems
  • Dual Lagrange multipliers
  • Inexact primal-dual active set strategy
  • Nonlinear multigrid method
  • Semismooth newton methods

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

A primal-dual active set algorithm for three-dimensional contact problems with Coulomb friction. / Hüeber, S.; Stadler, Georg; Wohlmuth, B. I.

In: SIAM Journal on Scientific Computing, Vol. 30, No. 2, 2007, p. 572-596.

Research output: Contribution to journalArticle

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