A scalable FETI-DP algorithm for a coercive variational inequality

We develop an optimal algorithm for the numerical solution of coercive variational inequalities, by combining FETI algorithms of dual-primal type with recent results for bound constrained quadratic programming problems. The discretized version of the model problem, obtained by using the FETI-DP methodology, is reduced by the duality theory of convex optimization to a quadratic programming problem with bound constraints. The resulting problem is solved by a new algorithm with a known rate of convergence given in terms of the spectral condition number of the quadratic problem. We present convergence bounds that guarantee the scalability of the algorithm. These results are confirmed by numerical experiments.