{
  "id": "1911.08954",
  "version": "v1",
  "published": "2019-11-20T15:01:55.000Z",
  "updated": "2019-11-20T15:01:55.000Z",
  "title": "Basic Ideas and Tools for Projection-Based Model Reduction of Parametric Partial Differential Equations",
  "authors": [
    "Gianluigi Rozza",
    "Martin Hess",
    "Giovanni Stabile",
    "Marco Tezzele",
    "Francesco Ballarin"
  ],
  "comment": "Book chapter to be published in the \"Handbook for Model Reduction\"",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions, offline-online decomposition and error estimation is introduced. Several tools for geometry parametrizations, such as free form deformation, radial basis function interpolation and inverse distance weighting interpolation are explained. The empirical interpolation method is introduced as a general tool to deal with non-affine parameter dependency and non-linear problems. The discrete and matrix versions of the empirical interpolation are considered as well. Active subspaces properties are discussed to reduce high-dimensional parameter spaces as a pre-processing step. Several examples illustrate the methodologies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-20T15:01:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parametric partial differential equations",
      "projection-based model reduction",
      "basic ideas",
      "reduce high-dimensional parameter spaces",
      "radial basis function interpolation"
    ],
    "tags": [
      "book chapter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}