Scalable FETI with optimal dual penalty for a variational inequality

The FETI method with the natural coarse grid is combined with the penalty method to develop an efficient solver for elliptic variational inequalities. A proof is given that a prescribed bound on the norm of feasibility of solution may be achieved with a value of the penalty parameter that does not depend on the discretization parameter and that an approximate solution with the prescribed bound on violation of the Karush-Kuhn-Tucker conditions may be found in a number of steps that does not depend on the discretization parameter. Results of numerical experiments with parallel solution of a model problem discretized by up to more than eight million of nodal variables are in agreement with the theory and demonstrate numerically both optimality of the penalty and scalability of the algorithm presented