rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Reduced basis methods for partial differential equations
    sub title: an introduction
  name:
    name part: Quarteroni, Alfio
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Manzoni, Andrea
    role:
      role term: author.
  name:
    name part: Negri, Federico
    role:
      role term: author.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: sz
    date issued: 2016
    copyright date: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: xi, 296 pages : illustrations (some color) ; 24 cm.
  abstract: This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing.
  table of contents: 1 Introduction -- 2 Representative problems: analysis and (high-fidelity) approximation -- 3 RB method: basic principle, basic properties -- 4 On the algebraic and geometric structure of RB methods -- 5 The theoretical rationale behind -- 6 Construction of RB spaces by SVD-POD -- 7 Construction of RB spaces by the greedy algorithm-- 8 RB methods in Action: Setting up the problem -- 9 RB methods in Action: Computing the solution -- 10 Extension to Nonaffine problem -- 11 Extension to nonlinear problems -- 12 Reduction and control -- Appendix A Basic theoretical tools.
  note: Alfio Quarteroni, Andrea Manzoni, Federico Negri.
  note: Includes bibliographical references (pages 281-292) and index.
  subject:
    topic: Differential equations, Partial
  subject:
    topic: Differential equations, Partial
  subject:
    topic: System von partiellen Differentialgleichungen
  classification: QA377 .Q378 2016
  classification: 515/.353
  related item:
    title info:
      title: Unitext ; 92
  identifier: 9783319154305
  identifier: 3319154303
  identifier: 9783319154312
  identifier: 2015930287
  record info:
    record content source: BTCTA
    record creation date: 150107
    record change date: 20190718162713.0
    record identifier: in00004053083
    language of cataloging:
      language term: eng