
Higher Order Dynamic Mode Decomposition and Its Applications
- 1st Edition - September 22, 2020
- Imprint: Academic Press
- Authors: Jose Manuel Vega, Soledad Le Clainche
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 1 9 7 4 3 - 1
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 2 2 7 6 6 - 4
Higher Order Dynamic Mode Decomposition and Its Applications provides detailed background theory, as well as several fully explained applications from a range of industria… Read more

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Request a sales quoteHigher Order Dynamic Mode Decomposition and Its Applications provides detailed background theory, as well as several fully explained applications from a range of industrial contexts to help readers understand and use this innovative algorithm. Data-driven modelling of complex systems is a rapidly evolving field, which has applications in domains including engineering, medical, biological, and physical sciences, where it is providing ground-breaking insights into complex systems that exhibit rich multi-scale phenomena in both time and space.
Starting with an introductory summary of established order reduction techniques like POD, DEIM, Koopman, and DMD, this book proceeds to provide a detailed explanation of higher order DMD, and to explain its advantages over other methods. Technical details of how the HODMD can be applied to a range of industrial problems will help the reader decide how to use the method in the most appropriate way, along with example MATLAB codes and advice on how to analyse and present results.
- Includes instructions for the implementation of the HODMD, MATLAB codes, and extended discussions of the algorithm
- Includes descriptions of other order reduction techniques, and compares their strengths and weaknesses
- Provides examples of applications involving complex flow fields, in contexts including aerospace engineering, geophysical flows, and wind turbine design
MSc students and researchers
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- Biography
- Professor José M. Vega
- Doctor Soledad Le Clainche
- Preface
- References
- Chapter 1: General introduction and scope of the book
- Abstract
- 1.1. Introduction to post-processing tools
- 1.2. Introduction to reduced order models
- 1.3. Organization of the book
- 1.4. Some concluding remarks
- 1.5. Annexes to Chapter 1
- References
- Chapter 2: Higher order dynamic mode decomposition
- Abstract
- 2.1. Introduction to standard DMD and HODMD
- 2.2. DMD and HODMD: methods and algorithms
- 2.3. Periodic and quasi-periodic phenomena
- 2.4. Some toy models
- 2.5. Some concluding remarks
- 2.6. Annexes to Chapter 2
- References
- Chapter 3: HODMD applications to the analysis of flight tests and magnetic resonance
- Abstract
- 3.1. Introduction to flutter in flight tests
- 3.2. Introduction to nuclear magnetic resonance
- 3.3. Some concluding remarks
- 3.4. Annexes to Chapter 3
- References
- Chapter 4: Spatio-temporal Koopman decomposition
- Abstract
- 4.1. Introduction to the spatio-temporal Koopman decomposition method
- 4.2. Traveling waves and standing waves
- 4.3. The STKD method
- 4.4. Some key points about the use of the STKD method
- 4.5. Some toy models
- 4.6. Some concluding remarks
- 4.7. Annexes to Chapter 4
- References
- Chapter 5: Application of HODMD and STKD to some pattern forming systems
- Abstract
- 5.1. Introduction to pattern forming systems
- 5.2. The one-dimensional CGLE
- 5.3. Thermal convection
- 5.4. Some concluding remarks
- 5.5. Annexes to Chapter 5
- References
- Chapter 6: Applications of HODMD and STKD in fluid dynamics
- Abstract
- 6.1. Introduction to fluid dynamics and global instability analysis
- 6.2. The two- and three-dimensional cylinder wake
- 6.3. Flow structures in the three-dimensional cylinder wake
- 6.4. The zero-net-mass-flux jet
- 6.5. Exercise: apply HODMD to analyze the three-dimensional cylinder wake
- 6.6. Some concluding remarks
- 6.7. Annexes to Chapter 6
- References
- Chapter 7: Applications of HODMD and STKD in the wind industry
- Abstract
- 7.1. On the relevance of extracting spatio-temporal patterns in wind turbine wakes
- 7.2. Flow structures in vertical wind turbines using the HODMD method
- 7.3. Analysis of the flow structures in a wind turbine with horizontal axis using STKD
- 7.4. LiDAR experimental data: wind velocity spatial predictions
- 7.5. Some concluding remarks
- 7.6. Annexes to Chapter 7
- References
- Chapter 8: HODMD and STKD as data-driven reduced order models
- Abstract
- 8.1. Introduction to data driven reduced order models
- 8.2. Data-driven reduced order models based on HODMD and STKD
- 8.3. Data-driven adaptive ROM: HODMD on the Fly
- 8.4. Exercises: data-driven reduced order models for the Lorenz system
- 8.5. Some concluding remarks
- 8.6. Annexes to Chapter 8
- References
- Chapter 9: Conclusions
- Abstract
- 9.1. Brief summary of the content of the book
- 9.2. The HODMD method
- 9.3. The STKD method
- 9.4. Scientific and industrially oriented applications
- References
- References
- References
- Index
- Edition: 1
- Published: September 22, 2020
- Imprint: Academic Press
- No. of pages: 320
- Language: English
- Paperback ISBN: 9780128197431
- eBook ISBN: 9780128227664
JV
Jose Manuel Vega
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