{
  "id": "1811.03839",
  "version": "v1",
  "published": "2018-11-09T09:57:14.000Z",
  "updated": "2018-11-09T09:57:14.000Z",
  "title": "Multilevel Schwarz preconditioners for singularly perturbed symmetric reaction-diffusion systems",
  "authors": [
    "José Pablo Lucero Lorca",
    "Guido Kanschat"
  ],
  "comment": "19 pages, 5 tables",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We present robust and highly parallel multilevel non-overlapping Schwarz preconditioners, to solve an interior penalty discontinuous Galerkin finite element discretization of a system of steady state, singularly perturbed reaction-diffusion equations with a singular reaction operator, using a GMRES solver. We provide proofs of convergence for the two-level setting and the multigrid V-cycle as well as numerical results for a wide range of regimes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-09T09:57:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N55",
      "65N30",
      "65J10",
      "65F08"
    ],
    "keywords": [
      "singularly perturbed symmetric reaction-diffusion systems",
      "multilevel schwarz preconditioners",
      "galerkin finite element discretization",
      "penalty discontinuous galerkin finite",
      "multilevel non-overlapping schwarz preconditioners"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}