{
  "id": "2005.09760",
  "version": "v1",
  "published": "2020-05-19T21:23:20.000Z",
  "updated": "2020-05-19T21:23:20.000Z",
  "title": "Some remarks on a coupling method for the practical computation of homogenized coefficients",
  "authors": [
    "Olga Gorynina",
    "Claude Le Bris",
    "Frédéric Legoll"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We numerically investigate, and improve upon, a computational approach originally introduced in [Cottereau, IJNME 2013] which aims at evaluating the effective coefficient of a medium modelled by a highly oscillatory coefficient. This computational approach is based on a Arlequin type coupling. It combines the original fine-scale description of the medium (modelled by an oscillatory coefficient) with an effective description (modelled by a constant coefficient) and optimizes upon the coefficient of the effective medium to best fit the response of the actual heterogeneous medium using a purely homogeneous medium. We present here a mathematical formalization of the approach along with various improvements of the algorithms, in order to obtain a procedure as efficient as possible. Representative numerical results demonstrate the added value of our approach in comparison to the original approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-19T21:23:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "practical computation",
      "homogenized coefficients",
      "coupling method",
      "computational approach",
      "original fine-scale description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}