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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