{
  "id": "2405.11203",
  "version": "v1",
  "published": "2024-05-18T07:12:38.000Z",
  "updated": "2024-05-18T07:12:38.000Z",
  "title": "A robust solver for H(curl) convection-diffusion and its local Fourier analysis",
  "authors": [
    "Jindong Wang",
    "Shuonan Wu"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-18T07:12:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F10",
      "65N30",
      "65N55",
      "35Q60"
    ],
    "keywords": [
      "local fourier analysis",
      "robust solver",
      "convection-diffusion problems",
      "efficient multigrid solver",
      "lexicographic gauss-seidel smoother"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}