Higher order dynamic mode decomposition and its applications /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Vega, Jos�e Manuel, 1974- (Autor), Le Clainche, Soledad (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: London, United Kingdom : Academic Press, an imprint of Elsevier, [2021]
Temas:
Decomposition (Mathematics)
Decomposition method.
D�ecomposition (Math�ematiques)
Decomposition method
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Preface
  • 1 General introduction and scope of the book
  • 1.1 Introduction to post-processing tools
  • 1.1.1 Singular value decomposition
  • 1.1.2 A toy model to illustrate SVD
  • 1.1.3 Proper orthogonal decomposition
  • 1.1.4 Higher order SVD
  • 1.1.5 A toy model to illustrate HOSVD
  • 1.1.6 Applications of SVD and HOSVD
  • 1.2 Introduction to reduced order models
  • 1.2.1 Data-driven ROMs
  • 1.2.2 Projection-based ROMs; 1.3 Organization of the book
  • 1.4 Some concluding remarks
  • 1.5 Annexes to Chapter 1
  • A. Compact SVD
  • B. Truncated SVD
  • C. Economy HOSVD
  • D. Compact HOSVD
  • E. Truncated HOSVD
  • 2 Higher order dynamic mode decomposition
  • 2.1 Introduction to standard DMD and HODMD
  • 2.2 DMD and HODMD: methods and algorithms
  • 2.2.1 The standard (optimized) DMD method: the DMD-1 algorithm
  • 2.2.2 The DMD-d algorithm with d>1
  • 2.2.3 HODMD for spatially multidimensional data, involving more than one spatial variables
  • 2.2.4 Iterative HODMD; 2.2.5 Some key points to successfully use the DMD-d algorithm with d>=1
  • 2.3 Periodic and quasi-periodic phenomena
  • 2.3.1 Approximate commensurability
  • 2.3.2 Semi-analytic representation of periodic dynamics and invariant periodic orbits in phase space
  • 2.3.3 Semi-analytic representation of quasi-periodic dynamics and the associated invariant tori in phase space
  • 2.4 Some toy models
  • 2.5 Some concluding remarks
  • 2.6 Annexes to Chapter 2
  • A. HODMD algorithm: the main program
  • B. DMD-d algorithm
  • C. DMD-1 algorithm
  • D. Reconstruction of the original eld; E. Approximate commensurability
  • 3 HODMD applications to the analysis of ight tests and magnetic resonance
  • 3.1 Introduction to utter in ight tests
  • 3.1.1 Training the method using a toy model for ight tests
  • 3.1.2 Using the method in actual ight tests experimental data
  • 3.2 Introduction to nuclear magnetic resonance
  • 3.2.1 Training the method using a magnetic resonance toy model
  • 3.2.2 Using the method with synthetic magnetic resonance experimental data
  • 3.3 Some concluding remarks
  • 3.4 Annexes to Chapter 3
  • A. Flight test experiments: toy model; B. Nuclear magnetic resonance: toy model
  • 4 Spatio-temporal Koopman decomposition
  • 4.1 Introduction to the spatio-temporal Koopman decomposition method
  • 4.2 Traveling waves and standing waves
  • 4.3 The STKD method
  • 4.3.1 A scalar state variable in one space dimension
  • 4.3.2 Vector state variable with one longitudinal and one transverse coordinate
  • 4.3.3 Vector state variable with two transverse and one longitudinal coordinates
  • 4.3.4 Vector state variable with one transverse and two longitudinal coordinates
  • 4.4 Some key points about the use of the STKD method

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