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

• Author(s): Hüeber, Stefan ; Stadler, Georg ; Wohlmuth, Barbara I.
• Date: 2006
• Persistent ID: http://hdl.handle.net/10316/11350
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): 3D Coulomb friction; Contact problems; Dual Lagrange multipliers; Inexact primal-dual active set strategy; Semismooth Newton methods; Nonlinear multigrid method
• Document Type: Preprint
• Language: English

Description

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 3D 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 is applied, and local superlinear convergence can be observed. 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. Deutsche Forschungsgemeinschaft, SFB 404, B8, SPP 1146