NDLI: Fourier Series for Accurate, Stable, Reduced-Order Models in Large-Scale Linear Applications

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Willcox, K. Megretski, A.
Copyright Year	2005
Abstract	A new method, Fourier model reduction, for obtaining stable, accurate, low-order models of very large linear systems is presented. The technique draws on traditional control and dynamical system concepts and utilizes them in a way which is computationally very efficient. Discrete-time Fourier coefficients of the large system are calculated and used to construct a reduced-order model that preserves stability properties of the original system. Many coefficients can be calculated, which results in a very accurate representation of the system dynamics, but only a single factorization of the large system is required. The resulting system can be further reduced using explicit formulae for balanced truncation. The method is applied to two computational fluid dynamic systems, which model unsteady motion of a two-dimensional subsonic airfoil and unsteady flow in a supersonic diffuser. In both cases, the new method is found to work extremely well. Results are compared to models developed using the proper orthogonal decomposition and Arnoldi method. In comparison with these widely used techniques, the new method is computationally more efficient, preserves the stability of the original system, uses both input and output information, and, for smooth transfer functions, is valid over a wide range of frequencies.
Starting Page	944
Ending Page	962
Page Count	19
File Format	PDF
ISSN	10648275
DOI	10.1137/S1064827502418768
e-ISSN	10957197
Issue Number	3
Volume Number	26
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	Fourier coefficients, Fourier series of functions with special properties, special Fourier series computational fluid dynamics Dynamical systems in fluid mechanics, oceanography and meteorology model reduction Fourier series Other numerical methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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