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The Proper Generalized Decomposition for Advanced Numerical Simulations - Francisco Chinesta, Roland Keunings, Adrien Leygue

The Proper Generalized Decomposition for Advanced Numerical Simulations

A Primer
Buch | Softcover
XIII, 117 Seiten
2013 | 2014
Springer International Publishing (Verlag)
978-3-319-02864-4 (ISBN)
CHF 74,85 inkl. MwSt

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.

1 Introduction.- 2 PGD solution of the Poisson equation.- 3 PGD versus SVD.- 4 The transient diffusion equation.- 5 Parametric models.- 6 Advanced topics.

Erscheint lt. Verlag 18.10.2013
Reihe/Serie SpringerBriefs in Applied Sciences and Technology
Zusatzinfo XIII, 117 p. 34 illus., 8 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 213 g
Themenwelt Informatik Weitere Themen CAD-Programme
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Technik Maschinenbau
Schlagworte high-dimensional problems • numerical simulation • Partial differential equations • reduced-order modelling • Separated representations
ISBN-10 3-319-02864-2 / 3319028642
ISBN-13 978-3-319-02864-4 / 9783319028644
Zustand Neuware
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