A robust solver for H(curl) convection-diffusion and its local Fourier analysis
<|reference_start|>A robust solver for H(curl) convection-diffusion and its local Fourier analysis: In this paper, we present a robust and efficient multigrid solver based on an exponential-fitting discretization for 2D H(curl) convection-diffusion problems. By leveraging an exponential identity, we characterize the kernel of H(curl) convection-diffusion problems and design a suitable hybrid smoother. This smoother incorporates a lexicographic Gauss-Seidel smoother within a downwind type and smoothing over an auxiliary problem, corresponding to H(grad) convection-diffusion problems for kernel correction. We analyze the convergence properties of the smoothers and the two-level method using local Fourier analysis (LFA). The performance of the algorithms demonstrates robustness in both convection-dominated and diffusion-dominated cases.<|reference_end|>
@article{wang2024a,
    title={A robust solver for H(curl) convection-diffusion and its local Fourier
  analysis},
    author={Jindong Wang, Shuonan Wu},
    journal={arXiv preprint arXiv:2405.11203},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.11203},
    primaryClass={math.NA cs.NA}
}