Non-overlapping Schwarz methods in time for parabolic optimal control problems
<|reference_start|>Non-overlapping Schwarz methods in time for parabolic optimal control problems: We present here the classical Schwarz method with a time domain decomposition applied to unconstrained parabolic optimal control problems. Unlike Dirichlet-Neumann and Neumann-Neumann algorithms, we find different properties based on the forward-backward structure of the optimality system. Variants can be found using only Dirichlet and Neumann transmission conditions. Some of these variants are only good smoothers, while others could lead to efficient solvers.<|reference_end|>
@article{gander2024non-overlapping,
    title={Non-overlapping Schwarz methods in time for parabolic optimal control
  problems},
    author={Martin Jakob Gander and Liu-Di Lu},
    journal={arXiv preprint arXiv:2408.12512},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.12512},
    primaryClass={math.NA cs.NA math.OC}
}