Solving the Signorini Problem on the Basis of Domain Decomposition Techniques

摘要

The finite element discretization of the Signorini Problem leads to a large scale constrained minimization problem. To improve the convergence rate of the projection method preconditioning must be developed. To be effective, the relative condition number of the system matrix with respect to the preconditioning matrix has to be small and the applications of the preconditioner as well as the projection onto the set of feasible elements have to be fast computable. In this paper, we show how to construct and analyze such preconditioners on the basis of domain decomposition tech- niques. The numerical results obtained for the Signorini problem as well as for contact problems in plane elasticity confirm the theoretical analysis quite well.