{
  "id": "2402.00364",
  "version": "v2",
  "published": "2024-02-01T06:02:54.000Z",
  "updated": "2025-01-13T13:23:13.000Z",
  "title": "A parallel domain decomposition method for solving elliptic equations on manifolds",
  "authors": [
    "Lizhen Qin",
    "Feng Wang",
    "Yun Wang"
  ],
  "comment": "Final version. To appear in SIAM Journal on Scientific Computing",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We propose a new numerical domain decomposition method for solving elliptic equations on compact Riemannian manifolds. One advantage of this method is its ability to bypass the need for global triangulations or grids on the manifolds. Additionally, it features a highly parallel iterative scheme. To verify its efficacy, we conduct numerical experiments on some $4$-dimensional manifolds without and with boundary.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-01-13T13:23:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "58J05",
      "65N55"
    ],
    "keywords": [
      "parallel domain decomposition method",
      "solving elliptic equations",
      "compact riemannian manifolds",
      "numerical domain decomposition method",
      "global triangulations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}