Two-level overlapping Schwarz preconditioners with universal coarse spaces for $2m$th-order elliptic problems
<|reference_start|>Two-level overlapping Schwarz preconditioners with universal coarse spaces for $2m$th-order elliptic problems: We propose a novel universal construction of two-level overlapping Schwarz preconditioners for $2m$th-order elliptic boundary value problems, where $m$ is a positive integer. The word "universal" here signifies that the coarse space construction can be applied to any finite element discretization for any $m$ that satisfies some common assumptions. We present numerical results for conforming, nonconforming, and discontinuous Galerkin-type finite element discretizations for high-order problems to demonstrate the scalability of the proposed two-level overlapping Schwarz preconditioners.<|reference_end|>
@article{park2024two-level,
    title={Two-level overlapping Schwarz preconditioners with universal coarse
  spaces for $2m$th-order elliptic problems},
    author={Jongho Park},
    journal={arXiv preprint arXiv:2403.18970},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.18970},
    primaryClass={math.NA cs.NA}
}