Improvements to the theoretical estimates of the Schwarz preconditioner with $\Delta$-GenEO coarse space for the indefinite Helmholtz problem
<|reference_start|>Improvements to the theoretical estimates of the Schwarz preconditioner with $\Delta$-GenEO coarse space for the indefinite Helmholtz problem: The purpose of this work is to improve the estimates for the $\Delta$-GenEO method from the paper "Overlapping Schwarz methods with GenEO coarse spaces for indefinite and nonself-adjoint problems" by N. Bootland, V. Dolean, I. G Graham, C. Ma, R. Scheichl (https://doi.org/10.1093/imanum/drac036) when applied to the indefinite Helmholtz equation. We derive k-dependent estimates of quantities of interest ensuring the robustness of the method.<|reference_end|>
@article{dolean2024improvements,
    title={Improvements to the theoretical estimates of the Schwarz preconditioner
  with $\Delta$-GenEO coarse space for the indefinite Helmholtz problem},
    author={Victorita Dolean, Mark Fry, Matthias Langer},
    journal={arXiv preprint arXiv:2403.18378},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.18378},
    primaryClass={math.NA cs.NA}
}