International Journal for Multiscale Computational Engineering

ISSN for PRINT: 1543-1649

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2005, Volume3

Issue 3

141 pages

Issue price - $178.00

William Gressick
Rensselaer Polytechnic Institute, Troy, NY 12180

John T. Wen
Rensselaer Polytechnic Institute, Troy, NY 12180

Jacob Fish
Multiscale Science and Engineering Center, Rensselaer Polytechnic Institute, Troy, NY 12189, USA

Large-scale finite element models are routinely used in design and optimization for complex engineering systems. However, the high model order prevents efficient exploration of the design space. Many model reduction methods have been proposed in the literature on approximating the high-dimensional model with a lower-order model. These methods typically replace a fine-scale model with a coarser-scale model in schemes, such as coarse graining, macromodeling, domain decomposition, and homogenization. This paper takes a systems perspective by stating the model reduction objective in terms of the approximation of the mapping between specified input and output variables. Methods from linear systems theory, including balance truncation and optimal Hankel norm approximation, are reviewed and compared to the standard modal truncation. For high-order systems, computational load, numerical stability, and memory storage become key considerations. We discuss several computationally more attractive iterative schemes that generate the approximate Gramian matrices needed in the model reduction procedure. A numerical example is also included to illustrate the model reduction algorithms discussed in the paper. We envision that these systems-oriented model reduction methods complementing the existing methods to produce low-order models suitable for design, optimization, and control.

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