An introduction to the proper orthogonal decomposition

By Anindya Chatterjee. 2000

1,293 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/87b4e8b5c620a6fadfbac1b1a5db04ff4badd317

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Citations in the corpus

Metric-Based Mathematical Derivation of Efficient Airfoil Design Variables (2015, methodology): “POD is a method to obtain a low-dimensional approximation to a high-dimensional space by the derivation of dominant components, or modes, and can be done by principal component analysis, Karhunen–Loeve decomposition, or singular value decomposition [43], though these methods can be shown to be equiv”
Multi-scale proper orthogonal decomposition of complex fluid flows (2018, methodology): “…the calculation of the POD modes of a discrete dataset could be formulated as a simple matrix factorization (see Kunisch & Volkwein 1999; Fahl 2000; Chatterjee 2000), in contrast to formulations based on statistics or dynamical system theory (such as Holmes et al. 1997; Noack et al. 2003; Berkooz…”
Higher Order Dynamic Mode Decomposition (2017, background): “If the RMS level of these errors is known beforehand, then they can be filtered out by an appropriate selection of the threshold ε1 appearing in (2.5), taking advantage of the well known [57] error-filtering ability of POD/SVD.”
The LATIN multiscale computational method and the Proper Generalized Decomposition (2010, methodology): “Such a decomposition makes this method present some similarities with the Proper Orthogonal Decomposition (POD [5]).”
Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis (2017, background): “Many papers exclusively present space-only POD (Sirovich, 1989; Moin & Moser, 1989; Holmes et al., 1997; Chatterjee, 2000; Rowley et al., 2004; Cordier & Bergmann, 2008; Rowley & Dawson, 2017), while one early review (George, 1988) considers only spectral POD.”
POD-DEIM model order reduction for strain softening viscoplasticity (2017, methodology): “To overcome this inefficiency, hyper-reduction methods, such as Missing Point Estimation [10], Gappy Proper Orthogonal Decomposition [11] and Discrete Empirical Interpolation Method (DEIM) [5], have been proposed to approximate the nonlinear contributions.”
The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains (2007, background): “The most striking features of the POD is its optimality: it provides the most efficient way of capturing the dominant components of an infinite-dimensional process with only a finite number of modes, often surprisingly few modes [3,22].”
A model-reduction approach in micromechanics of materials preserving the variational structure of constitutive relations (2016, methodology): “…such as the Proper Orthogonal Decomposition (POD) (also known under different names, Singular Value Decomposition, or Karhunen-Loève decomposition), are available in the literature to select the modes (Berkooz et al., 1993; Chatterjee, 2000; Chinesta and Cueto, 2014, and the references herein).”
Proper Orthogonal Decomposition for Linear-Quadratic Optimal Control (2013, methodology): “Proper orthogonal decomposition, model-order reduction, apriori and a-posteriori error analysis, linear-quadratic optimal control, primal-dual active set strategy.”
Numerical Modelling of Natural Draft Wet-Cooling Towers (2013, background): “The optimality lies in the fact that no other rank K approximation can be closer to U in the Frobenius norm or 2-norm [14].”