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This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena.
Synthesis of minimum roundoff noise fixed point digital filters
C. Mullis and R. Roberts · 1976
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Principal component analysis in linear systems: Controllability, observability, and model reduction
B. Moore · 1981
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Turbulence and the dynamics of coherent structures
L. Sirovich · 1987
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The proper orthogonal decomposition in the analysis of turbulent flows
G. Berkooz, P. Holmes, and J. L. Lumley · 1993
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Stability properties of POD-Galerkin approximations for the compressible Navier-Stokes equations
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Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods
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A Posteriori Error Bounds for Reduced-Basis Approximation of Parametrized Noncoercive and Nonlinear Elliptic Partial Differential Equations
K. Veroy, C. Prud’homme, D. Rovas, and A. Patera · 2003
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Upper and lower bounds for the tails of the distribution of the condition number of a gaussian matrix
J. Azaïs and M. Wschebor · 2004
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An ‘empirical interpolation’ method: application to efficient r educed-basis discretization of partial differential equations
M. Barrault, Y. Maday, N.-C. Nguyen, and A. Patera · 2004
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Model reduction for compressible flows using POD and Galerkin projection
C. W. Rowley, T. Colonius, and R. M. Murray · 2004
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Tails of condition number distributions
A. Edelman and B. Sutton · 2005
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Fast low-rank modifications of the thin singular value decomposition
M. Brand · 2006
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Numerical optimization
J. Nocedal and S. J. Wright · 2006
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Sparsity and incoherence in compressive sampling
E. Candès and J. Romberg · 2007
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Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
M. A. Grepl, Y. Maday, N. C. Nguyen, and A. T. Patera · 2007
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Dynamical low‐rank approximation
O. Koch and C. Lubich · 2007
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Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
G. Rozza, D. Huynh, and A. Patera · 2007
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On the stability of the reduced basis method for Stokes equations in parametrized domains
G. Rozza and K. Veroy · 2007
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Missing point estimation in models described by proper orthogonal decomposition
P. Astrid, S. Weiland, K. Willcox, and T. Backx · 2008
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ℋ 2 \mathcal{H}_{2} Model Reduction for Large-Scale Linear Dynamical Systems
S. Gugercin, A. Antoulas, and C. Beattie · 2008
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Reduced basis method for finite volume approximations of parametrized linear evolution equations
B. Haasdonk and M. Ohlberger · 2008
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Computational Investigation of Acoustics and Instabilities in a Longitudinal-Mode Rocket Combustor
R. Smith, M. Ellis, G. Xia, V. Sankaran, W. Anderson, and C. L. Merkle · 2008
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Exact matrix completion via convex optimization
E. J. Candès and B. Recht · 2009
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Dynamically orthogonal field equations for continuous stochastic dynamical systems
T. P. Sapsis and P. F. Lermusiaux · 2009
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Interpolatory model reduction of large-scale dynamical systems
A. Antoulas, C. Beattie, and S. Gugercin · 2010
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Nonlinear model reduction via discrete empirical interpolation
S. Chaturantabut and D. Sorensen · 2010
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Efficient non-linear model reduction via a least-squares Petrov–Galerkin projection and compressive tensor approximations
K. Carlberg, C. Bou-Mosleh, and C. Farhat · 2011
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Reduced basis approximation for nonlinear parametrized evolution equations based on empirical operator interpolation
Analysis of robust PCA via local incoherence
H. Zhang, Y. Zhou, and Y. Liang · 2015
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Robust model reduction by L1-norm minimization and approximation via dictionaries: application to nonlinear hyperbolic problems
R. Abgrall, D. Amsallem, and R. Crisovan · 2016
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A new selection operator for the discrete empirical interpolation method—improved a priori error bound and extensions
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A paradigm for data-driven predictive modeling using field inversion and machine learning
E. J. Parish and K. Duraisamy · 2016
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A Reduced Basis Technique for Long-Time Unsteady Turbulent Flows
L. Fick, Y. Maday, A. T. Patera, and T. Taddei · 2017
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M. Drohmann, B. Haasdonk, and M. Ohlberger · 2012
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A new error bound for reduced basis approximation of parabolic partial differential equations
K. Urban and A. T. Patera · 2012
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Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison
Z. Wang, I. Akhtar, J. Borggaard, and T. Iliescu · 2012
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Model reduction for nonlinear dynamical systems with parametric uncertainties
Y. B. Zhou · 2012
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Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing
M. Ohlberger and S. Rave · 2013
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Double greedy algorithms: Reduced basis methods for transport dominated problems
W. Dahmen, C. Plesken, and G. Welper · 2014
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Approximated Lax pairs for the reduced order integration of nonlinear evolution equations
J.-F. Gerbeau and D. Lombardi · 2014
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M. L. Frezzotti, S. D’Alessandro, B. Favini, and F. Nasuti · 2017
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Symplectic dynamical low rank approximation of wave equations with random parameters
E. Musharbash and F. Nobile · 2017
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h h and h p hp -adaptive Interpolation by Transformed Snapshots for Parametric and Stochastic Hyperbolic PDEs
G. Welper · 2017
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Interpolation of functions with parameter dependent jumps by transformed snapshots
G. Welper · 2017
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Reduced-Order Modeling of Model Rocket Combustors
J. Xu and K. Duraisamy · 2017
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M. L. Frezzotti, F. Nasuti, C. Huang, C. L. Merkle, and W. E. Anderson · 2018
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