000 03895nam a22005175i 4500
001 978-3-319-02865-1
003 DE-He213
005 20140220082512.0
007 cr nn 008mamaa
008 131008s2014 gw | s |||| 0|eng d
020 _a9783319028651
_9978-3-319-02865-1
024 7 _a10.1007/978-3-319-02865-1
_2doi
050 4 _aTA349-359
072 7 _aTGMD
_2bicssc
072 7 _aTEC009070
_2bisacsh
072 7 _aSCI041000
_2bisacsh
082 0 4 _a620.1
_223
100 1 _aChinesta, Francisco.
_eauthor.
245 1 4 _aThe Proper Generalized Decomposition for Advanced Numerical Simulations
_h[electronic resource] :
_bA Primer /
_cby Francisco Chinesta, Roland Keunings, Adrien Leygue.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXIII, 117 p. 34 illus., 8 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Applied Sciences and Technology,
_x2191-530X
505 0 _a1 Introduction -- 2 PGD solution of the Poisson equation -- 3 PGD versus SVD -- 4 The transient diffusion equation -- 5 Parametric models -- 6 Advanced topics.
520 _aMany 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 _aEngineering.
650 0 _aComputer aided design.
650 0 _aComputer science.
650 0 _aMechanics, applied.
650 1 4 _aEngineering.
650 2 4 _aTheoretical and Applied Mechanics.
650 2 4 _aComputational Science and Engineering.
650 2 4 _aComputer-Aided Engineering (CAD, CAE) and Design.
700 1 _aKeunings, Roland.
_eauthor.
700 1 _aLeygue, Adrien.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319028644
830 0 _aSpringerBriefs in Applied Sciences and Technology,
_x2191-530X
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-02865-1
912 _aZDB-2-ENG
999 _c92921
_d92921