{
  "id": "1106.0424",
  "version": "v1",
  "published": "2011-06-02T13:11:02.000Z",
  "updated": "2011-06-02T13:11:02.000Z",
  "title": "Field of values analysis of preconditioners for the Helmholtz equation in lossy media",
  "authors": [
    "Antti Hannukainen"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, we analyze the convergence of the preconditioned GMRES method for the first order finite element discretizations of the Helmholtz equation in media with losses. We consider a Laplace preconditioner, an inexact Laplace preconditioner and a two-level preconditioner. Our analysis is based on bounding the field of values of the preconditioned system matrix in the complex plane. The analysis takes the non-normal nature of the linear system naturally into account and allows us to easily consider certain type of inexact Laplace preconditioners via a perturbation argument. For the two-level preconditioner, our convergence analysis takes into account a media, which has not been considered in previous works.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-02T13:11:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N22"
    ],
    "keywords": [
      "helmholtz equation",
      "values analysis",
      "lossy media",
      "inexact laplace preconditioner",
      "first order finite element discretizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.0424H"
    }
  }
}