000 | 03895nam a22005175i 4500 | ||
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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 |
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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 |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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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 |