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.

翻译：本文针对二维H(curl)对流扩散问题，提出了一种基于指数拟合离散化的鲁棒高效多重网格求解器。通过利用指数恒等式，我们刻画了H(curl)对流扩散问题的核空间，并设计了一种合适的混合光滑器。该光滑器融合了顺风型字典序高斯-赛德尔光滑器以及辅助问题（对应核修正的H(grad)对流扩散问题）上的光滑处理。我们利用局部傅里叶分析（LFA）研究了光滑器及两层方法的收敛特性。算法性能在流主导与扩散主导情形下均展现出鲁棒性。