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:
    non sort: The
    title: Proper Generalized Decomposition for Advanced Numerical Simulations
    sub title: A Primer
  name:
    name part: Chinesta, Francisco.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Keunings, Roland.
    role:
      role term: author.
  name:
    name part: Leygue, Adrien.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 117 p. 34 illus., 8 illus. in color. online resource.
  abstract: Many problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom. Recently, the authors of this book and their collaborators have developed a novel technique, called Proper Generalized Decomposition (PGD) that has proven to be a significant step forward. The PGD builds by means of a successive enrichment strategy a numerical approximation of the unknown fields in a separated form. Although first introduced and successfully demonstrated in the context of high-dimensional problems, the PGD allows for a completely new approach for addressing more standard problems in science and engineering. Indeed, many challenging problems can be efficiently cast into a multi-dimensional framework, thus opening entirely new solution strategies in the PGD framework. For instance, the material parameters and boundary conditions appearing in a particular mathematical model can be regarded as extra-coordinates of the problem in addition to the usual coordinates such as space and time. In the PGD framework, this enriched model is solved only once to yield a parametric solution that includes all particular solutions for specific values of the parameters. The PGD has now attracted the attention of a large number of research groups worldwide. The present text is the first available book describing the PGD. It provides a very readable and practical introduction that allows the reader to quickly grasp the main features of the method. Throughout the book, the PGD is applied to problems of increasing complexity, and the methodology is illustrated by means of carefully selected numerical examples. Moreover, the reader has free access to the Matlab© software used to generate these examples.
  table of contents: 1 Introduction -- 2 PGD solution of the Poisson equation -- 3 PGD versus SVD -- 4 The transient diffusion equation -- 5 Parametric models -- 6 Advanced topics.
  note: by Francisco Chinesta, Roland Keunings, Adrien Leygue.
  subject:
    topic: Engineering
  subject:
    topic: Computer-aided engineering
  subject:
    topic: Computer mathematics
  subject:
    topic: Mechanics
  subject:
    topic: Mechanics, Applied
  subject:
    topic: Engineering
  subject:
    topic: Theoretical and Applied Mechanics
  subject:
    topic: Computational Science and Engineering
  subject:
    topic: Computer-Aided Engineering (CAD, CAE) and Design
  classification: TA349-359
  classification: 620.1
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: SpringerBriefs in Applied Sciences and Technology
  identifier: 9783319028651
  identifier: http://dx.doi.org/10.1007/978-3-319-02865-1
  record info:
    record creation date: 131008
    record change date: 20151030111100.0
    record identifier: 978-3-319-02865-1