Uzawa block relaxation domain decomposition method for the two-body contact problem with Tresca friction

✍ Scribed by Jonas Koko

• Book ID: 104013697
• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 733 KB
• Volume: 198
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2008.08.011

✦ Synopsis

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.