A Robin-robin Non-overlapping Domain Decomposition Method for an Elliptic Boundary Control Problem

A Robin-Robin non-overlapping domain decomposition method for an optimal boundary control problem associated with an elliptic boundary value problem is presented. The existence of the whole domain and subdomain optimal solutions is proven. The convergence of the subdomain optimal solutions to the whole domain optimal solution is shown. The optimality system is derived and a gradient-type method is defined for finding the optimal solution. A theoretic convergence result for the gradient method is established. The finite element version of the Robin-Robin non-overlapping domain decomposition method is analyzed and some numerical results by the method on both serial and parallel computers (using MPI) are presented.