{
  "id": "2408.17273",
  "version": "v1",
  "published": "2024-08-30T13:18:34.000Z",
  "updated": "2024-08-30T13:18:34.000Z",
  "title": "Overlapping subspaces and singular systems with application to Isogeometric Analysis",
  "authors": [
    "Andrea Bressan",
    "Massimiliano Martinelli",
    "Giancarlo Sangalli"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We propose a framework for solving partial differential equations (PDEs) motivated by isogeometric analysis (IGA) and local tensor-product splines. Instead of using a global basis for the solution space we use as generators the disjoint union of subspace bases. This leads to a potentially singular linear system, which is handled by a Krylov linear solver. The framework may offer computational advantages in dealing with spaces like Hierarchical B-splines, T-splines, and LR-splines.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-30T13:18:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "isogeometric analysis",
      "singular systems",
      "overlapping subspaces",
      "application",
      "krylov linear solver"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}