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A Dirichlet–Neumann type algorithm for contact problems with friction

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Computing and Visualization in Science


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. Numerical results illustrate the performance of our approach in 2D and 3D.

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Received: 20 March 2001 / Accepted: 1 February 2002

Communicated by P. Deuflhard

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Krause, R., Wohlmuth, B. A Dirichlet–Neumann type algorithm for contact problems with friction. Comput Visual Sci 5, 139–148 (2002).

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