Domain Decomposition Based Contact Solver
Free (open access)
J. Dobi´aˇs, S. Pt´ak, Z.Dost´al & V. Vondr´ak
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. Keywords: contact, domain decomposition, non-linear, Lagrange multipliers, finite element method. 1 Introduction Modelling contact phenomena is still a challenging problem of non-linear computational mechanics. The complexity of such problems arises from the fact that we do not knowthe regions in contact until we have run the problem. Their evaluations have to be part of the solution. In addition, the solution across the contact interface is non-smooth. In other words, a general contact problem is strongly non-linear and its reasonable solution in terms of a numerical technique, usually the finite element method, needs high quality software stemming from techniques exhibiting qualities like fast convergence rate, good parallel and numerical scalabilities, and so on. In 1991 Farhat and Roux  came up with a novel domain decomposition method called FETI (Finite Element Tearing and Interconnecting method). This
contact, domain decomposition, non-linear, Lagrange multipliers, finite element method.