The Proper Generalized Decomposition for Advanced Numerical Simulations A Primer /

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 develope...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Chinesta, Francisco (Συγγραφέας), Keunings, Roland (Συγγραφέας), Leygue, Adrien (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
Σειρά:SpringerBriefs in Applied Sciences and Technology,
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
LEADER 03950nam a22005295i 4500
001 978-3-319-02865-1
003 DE-He213
005 20151030111100.0
007 cr nn 008mamaa
008 131008s2014 gw | s |||| 0|eng d
020 |a 9783319028651  |9 978-3-319-02865-1 
024 7 |a 10.1007/978-3-319-02865-1  |2 doi 
040 |d GrThAP 
050 4 |a TA349-359 
072 7 |a TGMD  |2 bicssc 
072 7 |a TEC009070  |2 bisacsh 
072 7 |a SCI041000  |2 bisacsh 
082 0 4 |a 620.1  |2 23 
100 1 |a Chinesta, Francisco.  |e author. 
245 1 4 |a The Proper Generalized Decomposition for Advanced Numerical Simulations  |h [electronic resource] :  |b A Primer /  |c by Francisco Chinesta, Roland Keunings, Adrien Leygue. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2014. 
300 |a XIII, 117 p. 34 illus., 8 illus. in color.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a SpringerBriefs in Applied Sciences and Technology,  |x 2191-530X 
505 0 |a 1 Introduction -- 2 PGD solution of the Poisson equation -- 3 PGD versus SVD -- 4 The transient diffusion equation -- 5 Parametric models -- 6 Advanced topics. 
520 |a 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. 
650 0 |a Engineering. 
650 0 |a Computer-aided engineering. 
650 0 |a Computer mathematics. 
650 0 |a Mechanics. 
650 0 |a Mechanics, Applied. 
650 1 4 |a Engineering. 
650 2 4 |a Theoretical and Applied Mechanics. 
650 2 4 |a Computational Science and Engineering. 
650 2 4 |a Computer-Aided Engineering (CAD, CAE) and Design. 
700 1 |a Keunings, Roland.  |e author. 
700 1 |a Leygue, Adrien.  |e author. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783319028644 
830 0 |a SpringerBriefs in Applied Sciences and Technology,  |x 2191-530X 
856 4 0 |u http://dx.doi.org/10.1007/978-3-319-02865-1  |z Full Text via HEAL-Link 
912 |a ZDB-2-ENG 
950 |a Engineering (Springer-11647)