Uzawa Block Relaxation Domain Decomposition Method for the Two-Body Contact Problem With Tresca Friction

Jonas Koko (1)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes

We propose a Uzawa block relaxation domain decomposition method for a two-body contact problem with Tresca friction. We introduce auxiliary interface unknowns to transform the variational problem into a saddle-point problem. Applying a Uzawa block relaxation algorithm to the corresponding augmented Lagrangian functional we obtain a domain decomposition algorithm in which we have to solve two uncoupled linear elasticity subproblems in each iteration. The auxiliary unknowns are computed explicitly using Kuhn-Tucker conditions and Fenchel duality theory. Numerical experiments show the scalability of the domain decomposition algorithm on matching or nonmatching meshes for two- or three-dimensional contact problems.

Mots clés: Two-body contact; augmented Lagrangian; Kuhn-Tucker conditions; Fenchel duality; domain decomposition

Domaines: Analyse numérique [cs.NA]

Jonas Koko. Uzawa Block Relaxation Domain Decomposition Method for the Two-Body Contact Problem With Tresca Friction. Computer Methods in Applied Mechanics and Engineering, 2008, 198 (3-4), pp.Pages 420-431. ⟨10.1016/j.cma.2008.08.011⟩. ⟨hal-00678467⟩