Model Order Reduction Algorithm Research Articles

Simplification of Mathematical Models of Chemical Reaction Systems.

ADVERTISEMENT RETURN TO ISSUEArticleNEXTSimplification of Mathematical Models of Chemical Reaction SystemsMiles S. Okino and Michael L. MavrovouniotisView Author Information Department of Chemical Engineering, Northwestern University, Evanston, Illinois 60208-3120 Cite this: Chem. Rev. 1998, 98, 2, 391–408Publication Date (Web):February 28, 1998Publication History Received3 March 1997Revised13 January 1998Published online28 February 1998Published inissue 1 April 1998https://doi.org/10.1021/cr950223lCopyright © 1998 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views2377Altmetric-Citations243LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit Read OnlinePDF (248 KB) Get e-AlertsSUBJECTS:Chemical reactions,Kinetics,Order,Redox reactions,Transfer reactions Get e-Alerts

Reduced-order modeling of electromagnetic field interactions in unbounded domains truncated by perfectly matched layers

This letter presents the implementation of Berenger's perfectly matched layers and perfectly matched anisotropic absorbers in an electromagnetic field solver streamlined for the rapid simulation of vectorial electromagnetic interactions using Krylov space-based model order reduction algorithms. The proposed model and its computer implementation are validated through numerical simulation of electromagnetic wave propagation in metallic waveguides and associated components. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 17: 62–66, 1998.

Efficient formulation and model-order reduction for the transient simulation of three-dimensional VLSI interconnect

Accurately accounting for three-dimensional (3-D) geometry and distributed RC effects in on-chip interconnect is important for predicting crosstalk in memory cells, analog circuits, and regions of congested routing in digital circuits. In this paper we describe a multipole-accelerated, mixed surface-volume formulation, and a preconditioned model-order reduction algorithm for distributed RC, or electroquasistatic, simulation of 3-D integrated circuit interconnect. The difficulties arising from the ill conditioning inherent in the dynamic problem is effectively resolved by a combined surface-volume approach. Results are presented to demonstrate that the computational cost for extracting a complete reduced-order model is order N, where N is the number of surface unknowns. Finally, the multipole-accelerated code is used to investigate the accuracy of the one-dimensional diffusion equation for long RC lines.

On the σ - reciprocal system for model order reduction

In this paper a definition of the oσ-reciprocal system is introduced. This allows us to show that the generalized singular perturbation approximation method for model reduction is related to the direct truncation of the σ -reciprocal system. On the basis of this definition, two new model order reduction algorithms are presented. The suitability of the proposed reduction methods is illustrated by means of two numerical examples.

Second-order algorithm for optimal model order reduction

A second-order algorithm is given for optimal model order reduction of continuous single-input/single-output systems. Given a transfer function of order n, it finds the transfer function of a model of order m<n that minimizes the integral-square difference between the impulse responses of the two systems. It is shown that this is exactly equivalent to two other problems: 1) minimizing the integral-square difference between the frequency responses of the two systems and 2) minimizing the mean-square difference between the statistical steady-state responses of the two systems to a white-noise input. The algorithm is based on the known explicit solution of the governing Lyapunov equation, which yields analytical expressions for the first and second derivatives of the performance index with respect to the residues and poles of the reduced-order model. These derivatives are then used in a Newton-Raphson algorithm. The algorithm is applied to find exact solutions for four examples, one of which has an unstable mode. The examples corroborate previous research indicating that Moore's truncated balanced realization is not always close to the optimal reduced order model. Matching step response instead of impulse response requires only a slight change in the algorithm.