On the time-domain decomposition of parabolic optimal control problems

Abstract

Discretized parabolic control problems lead to very large systems of equations, because trajectories must be approximated forward and backward in time. It is therefore of interest to devise parallel solvers for such systems. In this paper, we propose an optimized Schwarz type method for decomposing the parabolic control problem in time, and show how to choose the optimized parameters to obtain the fastest convergence in the two subdomain case. The method of energy estimates is used to deduce the contraction rate. We illustrate the method for a problem constrained by the advection-diffusion equation.