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Preconditioned Uzawa Algorithm for Elastic Contact Problems
Author(s) -
Pop Nicolae
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810985
Subject(s) - augmented lagrangian method , discretization , finite element method , mathematics , saddle point , convergence (economics) , focus (optics) , nonlinear system , transformation (genetics) , algorithm , mathematical optimization , mathematical analysis , geometry , structural engineering , engineering , biochemistry , chemistry , physics , optics , quantum mechanics , economics , gene , economic growth
After finite element discretization of the elastic contact problems with friction, we obtain a big sparse non–symmetric and nonlinear systems of equations, and in many cases ill–conditioned. Solving these systems by direct methods or classical iterative methods are non efficient and with bad convergence properties. One way to overcome these difficulties is to use the preconditioned Uzawa–type algorithms. On this paper we focus on the transformation of the generalized Signorini elastic contact problems into a saddle point problem of some augmented Lagrangian functional and give a preconditioning technique for Uzawa algorithm. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)