Projector preconditioning and transformation of basis in FETI-DP algorithms for contact problems

Abstract

Two strategies, using edge averages, for FETI-DP (dual–primal finite element tearing and interconnecting) methods for contact problems are considered. The first one is a preconditioning technique by a conjugate projector, where the Lagrange multipliers corresponding to the variables of the coinciding edges are aggregated. The second one is an explicit transformation of basis introducing edge averages as new, additional primal variables. It is shown that both methods iterate in the same space and thus have the same rate of convergence. The theoretical result is confirmed by the solution of a model boundary variational inequality.