Preprint No. A-01-09

Rolf Krause, Barbara Wohlmuth

A Dirichlet-Neumann Type Algorithm for Contact Problems with Friction

Abstract: Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We introduce a new algorithm for the numerical solution of a nonlinear contact problem with Coulomb friction between linear elastic bodies. The discretization of the nonlinear problem is based on mortar techniques. We use a dual basis Lagrange multiplier space for the coupling of the different bodies. The boundary data transfer at the contact zone is essential for the algorithm. It is realized by a scaled mass matrix which results from the mortar discretization on non-matching triangulations. We apply a nonlinear block Gauß-Seidel method as iterative solver which can be interpreted as a Dirichlet-Neumann algorithm for the nonlinear problem. In each iteration step, we have to solve a linear Neumann problem and a nonlinear Signorini problem. The solution of the Signorini problem is realized in terms of monotone multigrid methods, \cite{RKornhuber_1997b,RK01}. Numerical results illustrate the performance of our approach in 2D and 3D.

Keywords: mortar finite elements, dual space, Dirichlet-Neumann algorithm, non-matching triangulations, multigrid methods, contact problems, linear elasticity

Mathematics Subject Classification (MSC2000): 65N30, 65N55, 74B10

Language: ENG

Available: Pr-A-01-09.ps, Pr-A-01-09.ps.gz

Contact: Rolf Krause, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (krause@math.fu-berlin.de)

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