Hilfe Warenkorb Konto Anmelden
 
 
   Schnellsuche   
     zur Expertensuche                      
Certified Reduced Basis Methods for Parametrized Partial Differential Equations
  Großes Bild
 
Certified Reduced Basis Methods for Parametrized Partial Differential Equations
von: Jan S Hesthaven, Gianluigi Rozza, Benjamin Stamm
Springer-Verlag, 2015
ISBN: 9783319224701
139 Seiten, Download: 3360 KB
 
Format:  PDF
geeignet für: Apple iPad, Android Tablet PC's Online-Lesen PC, MAC, Laptop

Typ: B (paralleler Zugriff)

 

 
eBook anfordern
Inhaltsverzeichnis

  Preface 7  
     References 8  
  Contents 10  
  1 Introduction 13  
     1.1 Historical Background and Perspectives 14  
     1.2 About this Book 17  
     1.3 Software Libraries with Support for Reduced Basis Algorithms and Applications 18  
     References 20  
  2 Parametrized Differential Equations 26  
     2.1 Parametrized Variational Problems 26  
        2.1.1 Parametric Weak Formulation 27  
        2.1.2 Inner Products, Norms and Well-Posedness of the Parametric Weak Formulation 27  
     2.2 Discretization Techniques 28  
     2.3 Toy Problems 30  
        2.3.1 Illustrative Example 1: Heat Conduction Part 1 31  
        2.3.2 Illustrative Example 2: Linear Elasticity Part 1 33  
     References 36  
  3 Reduced Basis Methods 37  
     3.1 The Solution Manifold and the Reduced Basis Approximation 38  
     3.2 Reduced Basis Space Generation 41  
        3.2.1 Proper Orthogonal Decomposition (POD) 42  
        3.2.2 Greedy Basis Generation 44  
     3.3 Ensuring Efficiency Through the Affine Decomposition 47  
     3.4 Illustrative Examples 49  
        3.4.1 Illustrative Example 1: Heat Conduction Part 2 49  
        3.4.2 Illustrative Example 2: Linear Elasticity Part 2 51  
     3.5 Summary of the Method 52  
     References 53  
  4 Certified Error Control 54  
     4.1 Introduction 54  
     4.2 Error Control for the Reduced Order Model 55  
        4.2.1 Discrete Coercivity and Continuity Constants of the Bilinear Form 55  
        4.2.2 Error Representation 56  
        4.2.3 Energy and Output Error Bounds 57  
        4.2.4 mathbbV-Norm Error Bounds 59  
        4.2.5 Efficient Computation of the a Posteriori Estimators 61  
        4.2.6 Illustrative Examples 1 and 2: Heat Conduction and Linear Elasticity Part 3 63  
     4.3 The Stability Constant 64  
        4.3.1 Min-?-approach 65  
        4.3.2 Multi-parameter Min-?-approach 66  
        4.3.3 Illustrative Example 1: Heat Conduction Part 4 66  
        4.3.4 The Successive Constraint Method (SCM) 68  
        4.3.5 A Comparitive Discussion 72  
     References 75  
  5 The Empirical Interpolation Method 76  
     5.1 Motivation and Historical Overview 76  
     5.2 The Empirical Interpolation Method 77  
     5.3 EIM in the Context of the RBM 81  
        5.3.1 Non-affine Parametric Coefficients 81  
        5.3.2 Illustrative Example 1: Heat Conduction Part 5 83  
        5.3.3 Illustrative Example 1: Heat Conduction Part 6 87  
     References 93  
  6 Beyond the Basics 95  
     6.1 Time-Dependent Problems 95  
        6.1.1 Discretization 96  
        6.1.2 POD-greedy Sampling Algorithm 98  
        6.1.3 A Posteriori Error Bounds for the Parabolic Case 100  
        6.1.4 Illustrative Example 3: Time-Dependent Heat Conduction 102  
     6.2 Geometric Parametrization 104  
        6.2.1 Illustrative Example 4: A 2D Geometric Parametrization for an Electronic Cooling Component 107  
        6.2.2 Illustrative Example 5: A 3D Geometric Parametrization for a Thermal Fin 111  
     6.3 Non-compliant Output 113  
        6.3.1 Illustrative Example 6: A 2D Graetz Problem with Non-compliant Output 115  
     6.4 Non-coercive Problems 118  
     6.5 Illustrative Example 7: A 3D Parametrized Graetz Channel 121  
     References 125  
  Appendix A Mathematical Preliminaries 127  
  Index 137  


nach oben


  Mehr zum Inhalt
Kapitelübersicht
Kurzinformation
Inhaltsverzeichnis
Leseprobe
Blick ins Buch
Fragen zu eBooks?

  Medientyp
  eBooks
  eJournal
  alle

  Navigation
Belletristik / Romane
Computer
Geschichte
Kultur
Medizin / Gesundheit
Philosophie / Religion
Politik
Psychologie / Pädagogik
Ratgeber
Recht
Reise / Hobbys
Sexualität / Erotik
Technik / Wissen
Wirtschaft

  Info
Hier gelangen Sie wieder zum Online-Auftritt Ihrer Bibliothek
© 2008-2022 ciando GmbH | Impressum | Kontakt | F.A.Q. | Datenschutz