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Published online by Cambridge University Press:  18 February 2021

Kevin W. Cassel
Affiliation:
Illinois Institute of Technology
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Print publication year: 2021

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References

Alvarez-Ramirez, J., Solis-Duan, J., and Puebla, H. (2005). Control of the Lorenz system: destroying the homoclinic orbits. Physics Letters A 338, 128140.Google Scholar
Aref, H. and Balachandar, S. (2018). A first course in computational fluid dynamics, Cambridge University Press.Google Scholar
Arnoldi, W. E. (1951). The principle of minimized iterations in the solution of the matrix eigenvalue problem. Quarterly of Applied Mathematics 9, 1729.Google Scholar
Asmar, N. H. (2005). Partial differential equations with Fourier series and boundary value problems, 2nd edition, Pearson Prentice Hall.Google Scholar
Benner, P., Gugercin, S., and Willcox, K. (2015). A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483531.CrossRefGoogle Scholar
Borrelli, F., Bemporad, A., and Morari, M. (2017). Predictive control for linear and hybrid systems, Cambridge University Press.Google Scholar
Boyd, S. and Vandenberghe, L. (2018). Introduction to applied linear algebra: vectors, matrices, and least squares, Cambridge University Press.CrossRefGoogle Scholar
Briggs, W. C., Henson, V. E., and McCormick, S. F. (2000). A multigrid tutorial, 2nd edition, SIAM.CrossRefGoogle Scholar
Brunton, S. L., Proctor, J. L., and Kutz, J. N. (2016). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences 113(15), 39323937.Google Scholar
Calafiore, G. C. and El Ghaoui, L. (2014). Optimization models, Cambridge University Press.Google Scholar
Canuto, C., Hussain, M., Quarteroni, A., and Zang, T. A. (1988). Spectral methods in fluid dynamics, Spring-Verlag.CrossRefGoogle Scholar
Cassel, K. W. (2013). Variational methods with applications in science and engineering, Cambridge University Press.CrossRefGoogle Scholar
Charru, F. (2011). Hydrodynamic instabilities, Cambridge University Press.CrossRefGoogle Scholar
Chung, T. J. (2010). Computational fluid dynamics, Cambridge University Press.Google Scholar
Demmel, J. W. (1997). Applied numerical linear algebra, SIAM.Google Scholar
Drazen, P. G. (1992). Nonlinear systems, Cambridge University Press.Google Scholar
Drazin, P. G. (2002). Introduction to hydrodynamic stability, Cambridge University Press.CrossRefGoogle Scholar
Duriez, T., Brunton, S., and Noack, B. R. (2017). Machine learning control – taming nonlinear dynamics and turbulence, Springer.Google Scholar
E, W. and Liu, J. G. (1996). Essentially compact schemes for unsteady viscous incompressible flows. Journal of Computational Physics 126, 122138.CrossRefGoogle Scholar
Farrell, B. F. and Ioannou, P. J. (1996). Generalized stability theory. Part 1: autonomous operators. Journal of the Atmospheric Sciences 53, 20252040.2.0.CO;2>CrossRefGoogle Scholar
Fasshauer, G. F. (2007). Meshfree approximation methods with MATLAB, World Scientific Publishing.Google Scholar
Ferziger, J. H., Peric, M., and Street, R. L. (2020). Computational methods for fluid dynamics, 4th edition, Springer-Verlag.Google Scholar
Fletcher, C. A. J. (1984). Computational Galerkin methods, Springer-Verlag.Google Scholar
Fletcher, C. A. J. (1991a). Computational techniques for fluid dynamics 1: fundamental and general techniques, Springer-Verlag.CrossRefGoogle Scholar
Fletcher, C. A. J. (1991b). Computational techniques for fluid dynamics 2: specific techniques for different flow categories, Springer-Verlag.CrossRefGoogle Scholar
Fletcher, R. and Reeves, C. M. (1964). Function minimization by conjugate gradients. Computer Journal 7, 149154.Google Scholar
Gilat, A. and Subramaniam, V. (2014). Numerical methods for engineers and scientists: an introduction with applications using MATLAB, 3rd edition, John Wiley and Sons.Google Scholar
Golub, G. H. and Van Loan, C. F. (2013). Matrix computations, 4th edition, Johns Hopkins University Press.Google Scholar
Greenberg, M. D. (1998). Advanced engineering mathematics, 2nd edition, Prentice Hall.Google Scholar
Gustafsson, B. (2008). High order difference methods for time dependent PDE, Springer-Verlag.Google Scholar
Hemati, M. S., Rowley, C. W., Deem, E. A., and Cattafesta, L. N. (2017). De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets. Theoretical and Computational Fluid Dynamics 31, 349368.CrossRefGoogle Scholar
Higham, N. J. (2002). Accuracy and stability of numerical algorithms, SIAM.CrossRefGoogle Scholar
Hildebrand, F. B. (1976). Advanced calculus for applications, Prentice Hall.Google Scholar
Holmes, P., Lumley, J. L., Berkooz, G., and Rowley, C. W. (2012). Turbulence, coherent structures, dynamical systems and symmetry, 2nd edition, Cambridge University Press.Google Scholar
Horn, R. A. and Johnson, C. R. (2013). Matrix analysis, 2nd edition, Cambridge University Press.Google Scholar
Incropera, F. P., DeWitt, D. P., Bergman, T. L., and Lavine, A. S. (2007). Fundamentals of heat and mass transfer, 6th edition, John Wiley and Sons.Google Scholar
Jeffrey, A. (2002). Advanced engineering mathematics, Harcourt/Academic Press.Google Scholar
Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Transactions of the ASME, Series D, Journal of Basic Engineering 82, 3545.Google Scholar
Kreyszig, E. (2011). Advanced engineering mathematics, 10th edition, John Wiley and Sons.Google Scholar
Kutz, J. N., Brunton, S. L., Brunton, B. W., and Proctor, J. L. (2016). Dynamic mode decomposition – data-driven modeling of complex systems, SIAM.Google Scholar
Lay, D. C., Lay, S. R., and McDonald, J. J. (2016). Linear algebra and its applications, 5th edition, Pearson Education Limited.Google Scholar
Lele, S. K. (1992). Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics 103, 1642.Google Scholar
Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of Atmospheric Sciences 20, 130141.Google Scholar
Lumley, J. L. (1967). The structure of inhomogeneous turbulence, In Yaglom, A. M. and Tatarski, V. I., editors, Atmospheric turbulence and wave propagation, 166–178. Nauka, Moscow.Google Scholar
Ma, Z., Ahuja, S., and Rowley, C. W. (2011). Reduced order models for control of fluids using the eigensystem realization algorithm. Theoretical and Computational Fluid Dynamics 25, 233247.CrossRefGoogle Scholar
Mancho, A. M., Wiggins, S., Curbelo, J., and Mendoza, C. (2013). Lagrangian descriptors: a method for revealing phase space structures of general time dependent dynamical systems. Communications in Nonlinear Science and Numerical Simulation 18, 35303557.Google Scholar
Meckes, E. S. and Meckes, M. W. (2018). Linear algebra, Cambridge University Press.CrossRefGoogle Scholar
Meiss, J. D. (2007). Differential dynamical systems, SIAM.CrossRefGoogle Scholar
Messac, A. (2015). Optimization in practice with MATLAB, Cambridge University Press.Google Scholar
Mezić, I. (2005). Spectral properties of dynamical systems, model reduction and decompositions. Nonlinear Dynamics 41, 309325.Google Scholar
Mezić, I. (2013). Analysis of fluid flows via spectral properties of the Koopman operator. Annual Review of Fluid Mechanics 45, 357378.Google Scholar
Miller, G. (2014). Numerical analysis for engineers and scientists, Cambridge University Press.Google Scholar
Moin, P. (2010). Fundamentals of engineering numerical analysis, 2nd edition, Cambridge University Press.Google Scholar
Morton, K. W. and Mayers, D. F. (1994). Numerical solution of partial differential equations, Cambridge University Press.Google Scholar
Nair, S. (2009). Introduction to continuum mechanics, Cambridge University Press.Google Scholar
Nayar, N. and Ortega, J. M. (1993). Computation of selected eigenvalues of generalized eigenvalue problems. Journal of Computational Physics 108, 814.Google Scholar
O’Neil, P. V. (2012). Advanced engineering mathematics, 7th edition, Cengage Learning.Google Scholar
Pikovsky, A. and Politi, A. (2016). Lyapunov exponents: a tool to explore complex dynamics, Cambridge University Press.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (2007). Numerical recipes – the art of scientific computing, 3rd edition, Cambridge University Press.Google Scholar
Radke, R. (1996). A MATLAB implementation of the implicitly restarted Arnoldi method for solving large-scale eigenvalue problems, MS Thesis, Rice University.Google Scholar
Rao, S. S. (2002). Applied numerical methods for engineers and scientists, Prentice Hall.Google Scholar
Reddy, J. N. (2013). An introduction to continuum mechanics, 2nd edition, Cambridge University Press.Google Scholar
Rowley, C. W. (2005). Model reduction for fluids using balanced proper orthogonal decomposition. International Journal of Bifurcation and Chaos 15(3), 9971013.Google Scholar
Rowley, C. W. and Dawson, S. M. (2017). Model reduction for flow analysis and control. Annual Review of Fluid Mechanics 49, 387417.Google Scholar
Saad, Y. (2003). Iterative methods for sparse linear systems, SIAM.Google Scholar
Saad, Y. and Schultz, M. H. (1986). A generalized minimum residual algorithm for solving nonsymmetric linear systems. SIAM Journal of Scientific and Statistical Computing 7, 856– 869.Google Scholar
Saltzman, B. (1962). Finite amplitude free convection as an initial value problem – I, Journal of the Atmospheric Sciences, 19, 329341.Google Scholar
Schmid, P. J. (2010). Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 528.Google Scholar
Sirovich, L. (1987). Turbulence and the dynamics of coherent structures, Parts I–III. Quarterly of Applied Mathematics XLV(3), 561–582.Google Scholar
Strang, G. (2006). Linear algebra and its applications, 4th edition, Cengage Learning.Google Scholar
Strang, G. (2016). Introduction to linear algebra, 5th edition, Wellesley Cambridge Press.Google Scholar
Tannehill, J. C., Anderson, D. A., and Pletcher, R. H. (1997). Computational fluid mechanics and heat transfer, Taylor and Francis.Google Scholar
Thomas, J. L., Diskin, B. and Brandt, A. T. (2003). Textbook multigrid efficiency for fluid simulations. Annual Review of Fluid Mechanics 35, 317340.Google Scholar
Tolstykh, A. I. (1994). High accuracy non-centered compact difference schemes for fluid dynamics applications, World Scientific Publishing.Google Scholar
Towne, A., Schmidt, O., and Colonius, T. (2018). Spectral proper-orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. Journal of Fluid Mechanics 847, 821867.Google Scholar
Trefethen, L. N. and Bau, D. B. (1997). Numerical linear algebra, SIAM.CrossRefGoogle Scholar
Trefethen, L. N. and Embree, M. (2005). Spectra and pseudospectra: the behavior of nonnormal matrices and operators, Princeton University Press.Google Scholar
Vanka, S. P. (1986). Block-implicit multigrid solution of Navier–Stokes equations in primitive variables. Journal of Computational Physics 65, 138158.Google Scholar
Viswanath, D. (2003). Symbolic dynamics and periodic orbits of the Lorenz attractor. Nonlinearity 16, 10351056.Google Scholar
Viswanath, D. (2007). Recurrent motions within plane Couette turbulence. Journal of Fluid Mechanics 580, 339358.Google Scholar
Yariv, A. and Yeh, P. (2007). Photonics: optical electronics in modern communications, 6th edition, Oxford University Press.Google Scholar

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  • References
  • Kevin W. Cassel, Illinois Institute of Technology
  • Book: Matrix, Numerical, and Optimization Methods in Science and Engineering
  • Online publication: 18 February 2021
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  • References
  • Kevin W. Cassel, Illinois Institute of Technology
  • Book: Matrix, Numerical, and Optimization Methods in Science and Engineering
  • Online publication: 18 February 2021
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  • References
  • Kevin W. Cassel, Illinois Institute of Technology
  • Book: Matrix, Numerical, and Optimization Methods in Science and Engineering
  • Online publication: 18 February 2021
Available formats
×