A Structured Quasi-Arnoldi procedure for model order reduction of second-order systems

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• 作者：Yung-Ta Li^a ; ^{ytli@math.nctu.edu.tw} ; Zhaojun Bai^b ; ^c ; ^{bai@cs.ucdavis.edu} ; Wen-Wei Lin^d ; ^{wwlin@math.ntu.edu.tw} ; Yangfeng Su^e ; ^{yfsu@fudan.edu.cn}
• 关键词：Model order reduction ; Moment matching ; Krylov subspace ; Arnoldi decomposition ; Structure-preserving
• 刊名：Linear Algebra and its Applications
• 出版年：2012
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：15 April, 2012
• 卷：436
• 期：8
• 页码：2780-2794
• 文件大小：439 K

摘要

Existing Krylov subspace-based structure-preserving model order reduction methods for the second-order systems proceed in two stages. The first stage is to generate a basis matrix of the underlying Krylov subspace. The second stage is to employ an explicit subspace projection to obtain a reduced-order model with a moment-matching property. An open problem is how to avoid explicit projection so that it will be efficient for truly large scale systems. In addition, it is also desired that a structure-preserving reduced system of order n matches maximum moments.

In this paper we propose a new procedure to compute a so-called Structured Quasi-Arnoldi (SQA) decomposition. Once the SQA decomposition is computed, a structure-preserving reduced-order model can be defined immediately from the decomposition without the explicit subspace projection. Furthermore, the reduced model of order n matches maximum moments. Numerical examples demonstrate that the transpose-free SQA-based reduced model is compatible with the two-sided structure-preserving explicit projection methods and is more accurate than the one-sided structure-preserving explicit projection methods due to the higher number of matched moments.