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We present new Dirichlet-Neumann and Neumann-Dirichlet algorithms with a timedomain decomposition applied to unconstrained parabolic optimal controlproblems. After a spatial semi-discretization, we use the Lagrange multiplierapproach to derive a coupled forward-backward optimality system, which can thenbe solved using a time domain decomposition. Due to the forward-backwardstructure of the optimality system, three variants can be found for theDirichlet-Neumann and Neumann-Dirichlet algorithms. We analyze theirconvergence behavior and determine the optimal relaxation parameter for eachalgorithm. Our analysis reveals that the most natural algorithms are actuallyonly good smoothers, and there are better choices which lead to efficientsolvers. We illustrate our analysis with numerical experiments.

New time domain decomposition methods for parabolic control problems I: Dirichlet-Neumann and Neumann-Dirichlet algorithms