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Primal and Dual Penalty Methods for Contact Problems with Geometrical Non‐linearities
Author(s) -
Vondrák Vít,
Dostál Zdeněk,
Dobiáš Jiří,
Pták Svatopluk
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510201
Subject(s) - feti , lagrange multiplier , penalty method , dual (grammatical number) , mathematical optimization , domain decomposition methods , nonlinear system , computer science , augmented lagrangian method , domain (mathematical analysis) , mathematics , mathematical analysis , finite element method , physics , structural engineering , engineering , art , literature , quantum mechanics
The nonlinearity caused by two or more bodies in contact is often source of computational difficulties. Probably the most popular solution method is based on direct iterations with the non‐penetration conditions imposed by the penalty method [1]. The method enables treatment of other non‐linearities such as in the case of large displacements. In this paper we are concerned with application of a variant of the FETI domain decomposition method that enforces feasibility of Lagrange multipliers by the penalty [5]. The dual penalty method, which has been shown to be optimal for small displacements, is used in inner loop of the algorithm that treats large displacements. We give results of numerical experiments that demonstrate high efficiency of the FETI method with the dual penalty. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)