Keywords: contact problems, variationally consistent discretization, TFETI, scalable algorithms.

Variationally consistent approximations of the nonpenetration conditions and friction laws was introduced (see Wohlmuth [1]) as a powerful tool for the discretization of contact problems, especially in the cases of a curved contact interface or nonmatching grids. In this paper we examine how this scheme complies with our recent development of scalable algorithms for contact problems. For the construction of mortar matrices we refer to the detailed paper [2].

We show that the constraint matrices arising from the variationally consistent approximation under natural restrictions are well conditioned for linear elements and satisfy the assumptions that guarantee the scalability of our algorithms.

The behaviour of the nummerical computation is shown on a two-dimensional example, which was implemented into our MatSol library of FETI based solvers for minimization problems and parallelized using the MatLab Parallel Computing Toolbox on a small cluster with 32 cores.

1

B.I. Wohlmuth, "Variationally consistent discretization schemes and numerical algorithms for contact problems", Acta Numerica, 20, 569-734, 2011.

2

A. Popp, M.W. Gee, W.A. Wall, "A finite deformation mortar contact formulation using a primaldual active set strategy", International Journal for Numerical Methods in Engineering, 79, 1354-1391 , 2009.

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