{
  "id": "2308.09007",
  "version": "v1",
  "published": "2023-08-17T14:22:36.000Z",
  "updated": "2023-08-17T14:22:36.000Z",
  "title": "A locally based construction of analysis-suitable $G^1$ multi-patch spline surfaces",
  "authors": [
    "Andrea Farahat",
    "Mario Kapl",
    "Aljaž Kosmač",
    "Vito Vitrih"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "Analysis-suitable $G^1$ (AS-$G^1$) multi-patch spline surfaces [4] are particular $G^1$-smooth multi-patch spline surfaces, which are needed to ensure the construction of $C^1$-smooth multi-patch spline spaces with optimal polynomial reproduction properties [16]. We present a novel local approach for the design of AS-$G^1$ multi-patch spline surfaces, which is based on the use of Lagrange multipliers. The presented method is simple and generates an AS-$G^1$ multi-patch spline surface by approximating a given $G^1$-smooth but non-AS-$G^1$ multi-patch surface. Several numerical examples demonstrate the potential of the proposed technique for the construction of AS-$G^1$ multi-patch spline surfaces and show that these surfaces are especially suited for applications in isogeometric analysis by solving the biharmonic problem, a particular fourth order partial differential equation, over them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-17T14:22:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "construction",
      "fourth order partial differential equation",
      "smooth multi-patch spline spaces",
      "smooth multi-patch spline surfaces",
      "optimal polynomial reproduction properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}