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¬The¬ Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer

¬The¬ Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer
Kataloginformation
Feldname Details
Vorliegende Sprache eng
Hinweise auf parallele Ausgaben 445719117 Druckausg.: ‡Chinesta, Francisco: ¬The¬ proper generalized decomposition for advanced numerical simulations
77286070X Druckausg.: ‡Chinesta, Francisco: ¬The¬ proper generalized decomposition for advanced numerical simulations
ISBN 978-3-319-02864-4
Name Chinesta, Francisco
Keunings, Roland
Name ANZEIGE DER KETTE Keunings, Roland
Name Leygue, Adrien
T I T E L ¬The¬ Proper Generalized Decomposition for Advanced Numerical Simulations
Zusatz zum Titel A Primer
Verlagsort Cham
Verlag Springer International Publishing
Erscheinungsjahr 2014
2014
Umfang Online-Ressource (XIII, 117 p. 34 illus., 8 illus. in color, online resource)
Reihe SpringerBriefs in Applied Sciences and Technology
Notiz / Fußnoten Description based upon print version of record
Weiterer Inhalt Preface; Contents; 1 Introduction; 1.1 Challenges in Numerical Simulation; 1.2 Model Reduction: Information Versus Relevant Information; 1.2.1 Extracting Relevant Information: The Proper Orthogonal Decomposition; 1.2.2 Building the POD Reduced-Order Model; 1.2.3 Illustrating the Construction of a Reduced-Order Model; 1.2.4 Discussion; 1.3 PGD at a glance; 1.4 Towards a New Paradigm in Computational Science; 1.5 A Brief Overview of PGD Applications; 1.5.1 Multidimensional Models; 1.5.2 Separating the Physical Space. 1.5.3 Parametric Models Defining Virtual Charts: A Route to Efficient Optimization, Inverse Identification and Real-time Simulation1.5.4 Real-time Simulation, DDDAS and More; 1.5.5 Open Issues and Further Developments; References; 2 PGD Solution of the Poisson Equation; 2.1 Progressive Construction of the Separated Representation; 2.1.1 Alternating Direction Strategy; 2.1.2 Stopping Criterion for the Enrichment Process; 2.1.3 Numerical Example; 2.2 Taking into Account Neumann Boundary Conditions; 2.3 Increasing the Complexity of the Case Study; 2.3.1 Non-Constant Source Term. 2.3.2 Non-Homogeneous Dirichlet Boundary Conditions2.3.3 Higher Dimensions and Separability of the Computational Domain; 2.4 Numerical Examples; 2.4.1 2D Heat Transfer Problem; 2.4.2 High-Dimensional Problem; References; 3 PGD Versus SVD; 3.1 Singular Value Decomposition and On-the-Fly Data Compression Using the PGD; 3.2 The PGD for Constructing Separated Approximations; 3.3 The PGD Approximation Constructor in Action; 3.4 The PGD for Data Post-Compression; 3.5 Numerical Example; References; 4 The Transient Diffusion Equation; 4.1 The One-Dimensional Transient Diffusion Equation. 4.1.1 Progressive Construction of the Separated Representation4.1.2 Alternating Direction Strategy; 4.1.3 Non-Incremental Versus Incremental Time Integrations; 4.2 Multi-Dimensional Transient Diffusion Equation; 4.3 Numerical Example; 4.4 Concluding Remarks; Reference; 5 Parametric Models; 5.1 Material Parameters as Extra-Coordinates; 5.1.1 Numerical Example; 5.2 Boundary Conditions as Extra-Coordinates; 5.2.1 Neumann Boundary Condition as Extra-Coordinate; 5.2.2 Dirichlet Boundary Condition as Extra-Coordinate; 5.2.3 Dirichlet and Neumann Boundary Conditions as Extra-Coordinates. 5.2.4 Non-Constant Neumann Boundary Conditions5.2.5 Non-Homogeneous Dirichlet Boundary Conditions; 5.3 Initial Conditions as Extra-Coordinates; 5.4 Computational Domain as Extra-Coordinates; References; 6 Advanced Topics; 6.1 Non-Linear Models; 6.1.1 PGD Strategies Based on Standard Linearization Schemes; 6.1.2 Discussion; 6.1.3 Interpolation of the Non-Linear Term; 6.1.4 Numerical Example; 6.2 Convective Stabilization; 6.2.1 Numerical Example; 6.3 Discrete Formulation of the PGD; 6.3.1 Example; 6.3.2 Alternating Direction Scheme; 6.4 Residual Minimization for Non-Symmetric Operators. 6.5 Numerical Example
Titelhinweis Druckausg.: ‡Chinesta, Francisco: ¬The¬ proper generalized decomposition for advanced numerical simulations
Druckausg.: ‡Chinesta, Francisco: ¬The¬ proper generalized decomposition for advanced numerical simulations
ISBN ISBN 978-3-319-02865-1
Klassifikation TGMD
TEC009070
SCI041000
*65-01
65N55
65M55
65M06
65N06
65M60
65N30
35K05
35J05
620.1015118
515.35
531.015118
511.8
004
TA349-359
Kurzbeschreibung 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 demonstrate
SWB-Titel-Idn 395820030
Signatur Springer E-Book
Bemerkungen Elektronischer Volltext - Campuslizenz
Elektronische Adresse $uhttp://dx.doi.org/10.1007/978-3-319-02865-1
Internetseite / Link Volltext
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Siehe auch Inhaltstext
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