{
  "id": "1907.07806",
  "version": "v1",
  "published": "2019-07-17T23:06:46.000Z",
  "updated": "2019-07-17T23:06:46.000Z",
  "title": "Optimization of a partial differential equation on a complex network",
  "authors": [
    "Martin Stoll",
    "Max Winkler"
  ],
  "comment": "20 pages, 4 figures",
  "categories": [
    "math.OC",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "Differential equations on metric graphs can describe many phenomena in the physical world but also the spread of information on social media. To efficiently compute the solution is a hard task in numerical analysis. Solving a design problem, where the optimal setup for a desired state is given, is even more challenging. In this work, we focus on the task of solving an optimization problem subject to a differential equation on a metric graph with the control defined on a small set of Dirichlet nodes. We discuss the discretization by finite elements and provide rigorous error bounds as well as an efficient preconditioning strategy to deal with the large-scale case. We show in various examples that the method performs very robustly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-17T23:06:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F08",
      "65N30",
      "49J20",
      "35R02"
    ],
    "keywords": [
      "partial differential equation",
      "complex network",
      "metric graph",
      "optimization problem subject",
      "design problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}