Duality based domain decomposition with proportioning for the solution of free boundary problems

Quadratic programming problems arising from the discretization of free boundary elliptic problems with the spatial domain comprising several subdomains are considered. An algorithm for the solution of these problems is proposed that combines our algorithm recently presented for the solution of quadratic programming problems with a duality-based domain decomposition method of the Neumann-Neumann type. The characteristic feature of the algorithm is that it reduces the problem to a sequence of well-conditioned auxiliary problems with the precision controlled by the norm of the unbalanced contact residual. The algorithm may be implemented with projections so that it is capable to drop and add many constraints whenever the active set is changed. Numerical experiments with simple model problems indicate that the algorithm is robust and efficient. The algorithm can prove useful in parallel computing environment.