A Parallel in Time Algorithm Based on ParaExp for Optimal Control Problems
<|reference_start|>A Parallel in Time Algorithm Based on ParaExp for Optimal Control Problems: We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping time-domain decomposition in which we combine the solution of homogeneous problems using exponential propagation with the local solutions of inhomogeneous problems. The algorithm yields a linear system whose matrix-vector product can be fully performed in parallel. We then propose a preconditioner to speed up the convergence of GMRES in the special cases of the heat and wave equations. Numerical experiments are provided to illustrate the efficiency of our preconditioners.<|reference_end|>
@article{kwok2024a,
    title={A Parallel in Time Algorithm Based on ParaExp for Optimal Control
  Problems},
    author={Felix Kwok (ULaval), Djahou N Tognon (SU, INRIA)},
    journal={arXiv preprint arXiv:2406.11478},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.11478},
    primaryClass={cs.DC cs.NA math.NA}
}