SpringerBriefs in Applied Sciences and Technology

The Proper Generalized Decomposition for Advanced Numerical Simulations

A Primer

Authors: Chinesta, Francisco, Keunings, Roland, Leygue, Adrien

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About this book

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 (6 chapters)

  • Introduction

    Chinesta, Francisco (et al.)

    Pages 1-24

  • PGD Solution of the Poisson Equation

    Chinesta, Francisco (et al.)

    Pages 25-46

  • PGD Versus SVD

    Chinesta, Francisco (et al.)

    Pages 47-56

  • The Transient Diffusion Equation

    Chinesta, Francisco (et al.)

    Pages 57-69

  • Parametric Models

    Chinesta, Francisco (et al.)

    Pages 71-88

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-02865-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-02864-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Proper Generalized Decomposition for Advanced Numerical Simulations
Book Subtitle
A Primer
Authors
Series Title
SpringerBriefs in Applied Sciences and Technology
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-02865-1
DOI
10.1007/978-3-319-02865-1
Softcover ISBN
978-3-319-02864-4
Series ISSN
2191-530X
Edition Number
1
Number of Pages
XIII, 117
Number of Illustrations and Tables
26 b/w illustrations, 8 illustrations in colour
Topics