This paper deals with the solution of the discretized quasistatic 3D Signorini problems with local Coulomb friction. After a time discretization we obtain a system of static contact problems with Coulomb friction. Each of these problems is decomposed by the TFETI domain decomposition method used in auxiliary contact problems with Tresca friction. The algebraic formulation of these problems in 3D leads to the quadratic programing with equality constraints together with box and separable quadratic constraints. For the solution we used the scalable algorithm SMALSE developed at our department. The efficiency of the method is demonstrated by results of numerical experiments with parallel solution of 3D contact problems of elasticity.

The paper is concerned with the application of a new variant of the FETI domain decomposition method called the Total FETI to the solution of contact problems by the finite element method. The basic idea is that both the compatibility between adjacent sub-domains and Dirichlet boundary conditions are enforced by the Lagrange multipliers with physical meaning of forces, while the displacements are eliminated. We introduce the Total FETI technique to solve the equations and inequalities governing the equilibrium of system of bodies in contact. Moreover, we show implementation of the method into a code which treats the material and geometric non-linear effects. Numerical experiments were carried out with our inhouse general purpose package PMD.