Reconstruction equations and the Karhunen—Loéve expansion for systems with symmetry

By Clarence W. Rowley, Jerrold E. Marsden. 2000

202 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ed3076adc1f3c78e0b3a202a888dece6e3dbe018

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. J. Nathan Kutz
2. Steven L. Brunton
3. Sanjay Lall
4. Linda R. Petzold
5. Muruhan Rathinam
6. Petr Krysl
7. Sonja Glavaski
8. Jerrold E. Marsden

In Numerical Analysis

1. Sanjay Lall
2. Sonja Glavaski
3. Jerrold E. Marsden
4. Linda R. Petzold
5. Muruhan Rathinam
6. Petr Krysl
7. Steven L. Brunton
8. J. Nathan Kutz

In Statistical and Nonlinear Physics

1. Steven L. Brunton
2. J. Nathan Kutz
3. Sanjay Lall
4. Clarence W. Rowley
5. Petr Krysl
6. Jerrold E. Marsden
7. Sonja Glavaski
8. Linda R. Petzold

Citations in the corpus

• A New Look at Proper Orthogonal Decomposition (2003, methodology): “Methods for combining reduction theory with POD have been developed in [23].”
• A subspace approach to balanced truncation for model reduction of nonlinear control systems (2002, methodology): “[10, 11] and other special structure present in the original system can be of great use, leading to reduced computational requirements and producing more accurate reduced-order models.”
• Multiresolution Dynamic Mode Decomposition (2015, background): “For dynamical cases exhibiting translation and/or rotation, Rowley and Marsden [22] formulated one of the only mathematical strategies to date to extract the lowdimensional embeddings.”
• Finite-dimensional control of nonlinear parabolic PDE systems with time-dependent spatial domains using empirical eigenfunctions (2001, methodology): “L expansion for PDE systems whose solutions contain traveling structures by exploiting symmetry ( Rowley and Marsden , 2000 ) .”
• Model reduction for real-time fluids (2006, methodology): “For flows with periodic boundaries, and with inherent symmetries within the flow dynamics , it is possible remove uniform translation modes [Rowley et al. 2003; Rowley and Marsden 2000].”
• Low-Dimensional Modelling of Turbulence Using the Proper Orthogonal Decomposition: A Tutorial (2005, methodology): “The method of Rowley and Marsden [40] was proposed for the low-dimensional modelling of systems with translational symmetry.”
• Structure-preserving model reduction for mechanical systems (2003, methodology): “Experience has shown that if a system has symmetry, then using travelling Karhunen–Loève bases can dramatically cut down the dimension of the reduced system; see, for example,[8,36] and references therein.”