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000723015 020__ $$a9783319028651$$qelectronic book
000723015 020__ $$a3319028650$$qelectronic book
000723015 020__ $$z9783319028644
000723015 020__ $$a3319028642
000723015 020__ $$a9783319028644
000723015 020__ $$a1306200210
000723015 020__ $$a9781306200219
000723015 0247_ $$a10.1007/978-3-319-02865-1$$2doi
000723015 035__ $$aSP(OCoLC)ocn862734238
000723015 035__ $$aSP(OCoLC)862734238
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000723015 049__ $$aISEA
000723015 050_4 $$aQA401
000723015 08204 $$a511.8$$223
000723015 1001_ $$aChinesta, Francisco,$$eauthor.
000723015 24514 $$aThe proper generalized decomposition for advanced numerical simulations$$h[electronic resource] :$$ba primer /$$cFrancisco Chinesta, Roland Keunings, Adrien Leygue.
000723015 264_1 $$aCham :$$bSpringer,$$c2014.
000723015 300__ $$a1 online resource (xiii, 117 pages) :$$billustrations (some color).
000723015 336__ $$atext$$btxt$$2rdacontent
000723015 337__ $$acomputer$$bc$$2rdamedia
000723015 338__ $$aonline resource$$bcr$$2rdacarrier
000723015 4901_ $$aSpringerBriefs in Applied Sciences and Technology,$$x2191-530X
000723015 504__ $$aIncludes bibliographical references.
000723015 5050_ $$aPGD solution of the Poisson equation -- PGD versus SVD -- The transient diffusion equation -- Parametric models -- Advanced topics.
000723015 506__ $$aAccess limited to authorized users.
000723015 520__ $$aMany problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom. Recently, the authors of this book and their collaborators have developed a novel technique, called Proper Generalized Decomposition (PGD) that has proven to be a significant step forward. The PGD builds by means of a successive enrichment strategy a numerical approximation of the unknown fields in a separated form. Although first introduced and successfully demonstrated in the context of high-dimensional problems, the PGD allows for a completely new approach for addressing more standard problems in science and engineering. Indeed, many challenging problems can be efficiently cast into a multi-dimensional framework, thus opening entirely new solution strategies in the PGD framework. For instance, the material parameters and boundary conditions appearing in a particular mathematical model can be regarded as extra-coordinates of the problem in addition to the usual coordinates such as space and time. In the PGD framework, this enriched model is solved only once to yield a parametric solution that includes all particular solutions for specific values of the parameters. The PGD has now attracted the attention of a large number of research groups worldwide. The present text is the first available book describing the PGD. It provides a very readable and practical introduction that allows the reader to quickly grasp the main features of the method. Throughout the book, the PGD is applied to problems of increasing complexity, and the methodology is illustrated by means of carefully selected numerical examples. Moreover, the reader has free access to the Matlab software used to generate these examples.
000723015 588__ $$aDescription based on online resource; title from PDF title page (SpringerLink, viewed October 14, 2013).
000723015 650_0 $$aMathematical models.
000723015 7001_ $$aKeunings, R.,$$eauthor.
000723015 7001_ $$aLeygue, Adrien,$$eauthor.
000723015 830_0 $$aSpringerBriefs in applied sciences and technology,$$x2191-530X
000723015 852__ $$bebk
000723015 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-02865-1$$zOnline Access$$91397441.1
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000723015 980__ $$aEBOOK
000723015 980__ $$aBIB
000723015 982__ $$aEbook
000723015 983__ $$aOnline
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