Nonlinear Monolithic Two-Level Schwarz Methods for the Navier-Stokes Equations
<|reference_start|>Nonlinear Monolithic Two-Level Schwarz Methods for the Navier-Stokes Equations: Nonlinear domain decomposition methods became popular in recent years since they can improve the nonlinear convergence behavior of Newton's method significantly for many complex problems. In this article, a nonlinear two-level Schwarz approach is considered and, for the first time, equipped with monolithic GDSW (Generalized Dryja-Smith-Widlund) coarse basis functions for the Navier-Stokes equations. Results for lid-driven cavity problems with high Reynolds numbers are presented and compared with classical global Newton's method equipped with a linear Schwarz preconditioner. Different options, for example, local pressure corrections on the subdomain and recycling of coarse basis functions are discussed in the nonlinear Schwarz approach for the first time.<|reference_end|>
@article{klawonn2024nonlinear,
    title={Nonlinear Monolithic Two-Level Schwarz Methods for the Navier-Stokes
  Equations},
    author={Axel Klawonn, Martin Lanser},
    journal={arXiv preprint arXiv:2409.03041},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.03041},
    primaryClass={math.NA cs.CE cs.NA}
}