{
  "id": "2108.09463",
  "version": "v1",
  "published": "2021-08-21T08:53:03.000Z",
  "updated": "2021-08-21T08:53:03.000Z",
  "title": "Heterogeneous multiscale methods for the Landau-Lifshitz equation",
  "authors": [
    "Lena Leitenmaier",
    "Olof Runborg"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper, we present a finite difference heterogeneous multiscale method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient. The approach combines a higher order discretization and artificial damping in the so-called micro problem to obtain an efficient implementation. The influence of different parameters on the resulting approximation error is discussed. Numerical examples for both periodic as well as more general coefficients are given to demonstrate the functionality of the approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-21T08:53:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M15",
      "35B27",
      "78M40"
    ],
    "keywords": [
      "landau-lifshitz equation",
      "finite difference heterogeneous multiscale method",
      "highly oscillatory diffusion coefficient",
      "higher order discretization",
      "resulting approximation error"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}