{
  "id": "1909.08215",
  "version": "v1",
  "published": "2019-09-18T05:22:12.000Z",
  "updated": "2019-09-18T05:22:12.000Z",
  "title": "Computational multiscale methods for first-order wave equation using mixed CEM-GMsFEM",
  "authors": [
    "Eric Chung",
    "Sai-Mang Pun"
  ],
  "comment": "17 pages, 5 figures",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper, we consider a pressure-velocity formulation of the heterogeneous wave equation and employ the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to solve this problem. The proposed method provides a flexible framework to construct crucial multiscale basis functions for approximating the pressure and velocity. These basis functions are constructed by solving a class of local auxiliary optimization problems over the eigenspaces that contain local information on the heterogeneity. Techniques of oversampling are adapted to enhance the computational performance. The first-order convergence of the proposed method is proved and illustrated by several numerical tests.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-18T05:22:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M60"
    ],
    "keywords": [
      "first-order wave equation",
      "computational multiscale methods",
      "crucial multiscale basis functions",
      "multiscale finite element method",
      "generalized multiscale finite element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}