A robust solver for H(curl) convection-diffusion and its local Fourier analysis

TL;DR

This paper introduces a robust multigrid solver for 2D H(curl) convection-diffusion problems using exponential-fitting discretization, a hybrid smoother, and local Fourier analysis to ensure efficiency across different regimes.

Contribution

It develops a novel multigrid solver with a hybrid smoother tailored for H(curl) convection-diffusion problems, analyzed via local Fourier analysis for robustness.

Findings

Solver is robust in convection- and diffusion-dominated regimes

Hybrid smoother effectively accelerates convergence

Local Fourier analysis confirms convergence properties

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.