New time domain decomposition methods for parabolic optimal control problems II: Neumann-Neumann algorithms
CoRR(2024)
摘要
We present new Neumann-Neumann algorithms based on a time domain
decomposition applied to unconstrained parabolic optimal control problems.
After a spatial semi-discretization, the Lagrange multiplier approach provides
a coupled forward-backward optimality system, which can be solved using a time
domain decomposition. Due to the forward-backward structure of the optimality
system, nine variants can be found for the Neumann-Neumann algorithms. We
analyze their convergence behavior and determine the optimal relaxation
parameter for each algorithm. Our analysis reveals that the most natural
algorithms are actually only good smoothers, and there are better choices which
lead to efficient solvers. We illustrate our analysis with numerical
experiments.
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