Coarse Spaces Based on Higher-Order Interpolation for Schwarz Preconditioners for Helmholtz Problems
<|reference_start|>Coarse Spaces Based on Higher-Order Interpolation for Schwarz Preconditioners for Helmholtz Problems: The development of scalable and wavenumber-robust iterative solvers for Helmholtz problems is challenging but also relevant for various application fields. In this work, two-level Schwarz domain decomposition preconditioners are enhanced by coarse space constructed using higher-order B\'ezier interpolation. The numerical results indicate numerical scalability and robustness with respect the wavenumber, as long as the wavenumber times the element size of the coarse mesh is sufficiently low.<|reference_end|>
@article{sieburgh2024coarse,
    title={Coarse Spaces Based on Higher-Order Interpolation for Schwarz
  Preconditioners for Helmholtz Problems},
    author={Erik Sieburgh, Alexander Heinlein, Vandana Dwarka and Cornelis Vuik},
    journal={arXiv preprint arXiv:2408.03571},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.03571},
    primaryClass={math.NA cs.NA}
}