Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v3.i3.60
pages 337-362

Order Reduction for Large-Scale Finite Element Models: A Systems Perspective

William Gressick
Rensselaer Polytechnic Institute, Troy, NY 12180
John T. Wen
Rensselaer Polytechnic Institute, Troy, NY 12180
Jacob Fish
Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027, USA

ABSTRACT

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.


Articles with similar content:

UNCERTAINTY QUANTIFICATION FOR MAXWELL'S EQUATIONS USING STOCHASTIC COLLOCATION AND MODEL ORDER REDUCTION
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 3
Judith Schneider, Peter Benner
ANALYSIS OF VARIANCE-BASED MIXED MULTISCALE FINITE ELEMENT METHOD AND APPLICATIONS IN STOCHASTIC TWO-PHASE FLOWS
International Journal for Uncertainty Quantification, Vol.4, 2014, issue 6
Guang Lin, Yalchin Efendiev, Lijian Jiang, Jia Wei
BIAS MINIMIZATION IN GAUSSIAN PROCESS SURROGATE MODELING FOR UNCERTAINTY QUANTIFICATION
International Journal for Uncertainty Quantification, Vol.1, 2011, issue 4
Vadiraj Hombal, Sankaran Mahadevan
A Model of a Certain Class of Dynamical Systems with Discrete State Space
Journal of Automation and Information Sciences, Vol.30, 1998, issue 2-3
Victor I. Ivanenko, Nikolay A. Zinchuk
THE MODAL IDENTIFICATION METHOD IN NONLINEAR HEAT TRANSFER PROBLEMS
International Heat Transfer Conference 13, Vol.0, 2006, issue
O. Balima, Daniel Petit, Jean-Bernard Saulnier, Manuel Girault, Yann Favennec