A robust solver for H(curl) convection-diffusion and its local Fourier analysis
Numerical Analysis
2024-05-21 v1 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2405.11203,
title = {A robust solver for H(curl) convection-diffusion and its local Fourier analysis},
author = {Jindong Wang and Shuonan Wu},
journal= {arXiv preprint arXiv:2405.11203},
year = {2024}
}