Title: Automated and efficient order selection in Krylov-based model order reduction

Authors: Mohammad Abid Bazaz; Mashuq-un-Nabi; S. Janardhanan

Addresses: Department of Electrical Engineering, National Institute of Technology, Srinagar, 190006, India ' Department of Electrical Engineering, Indian Institute of Technology, Delhi, 110016, India ' Department of Electrical Engineering, Indian Institute of Technology, Delhi, 110016, India

Abstract: Krylov-subspace-based model order reduction is one of the most widely used techniques for the reduction of very large systems, having sizes ranging typically from thousands to several millions. By projecting the large system dynamics onto an appropriate Krylov subspace, some of the leading moments of the reduced system transfer function can be made to implicitly match the corresponding moments of the original system. The iterative algorithms used for generating the orthogonal bases for the Krylov subspace have reliable numerical implementations involving matrix-vector multiplications exclusively. However, the selection of a suitable order of the reduced system is an adhoc procedure in these algorithms. This paper presents an efficient stopping criterion based on a new index, known as coefficient of numerical rank improvement, to automate the process of order selection in Krylov-based reduction procedures. Numerical experiments conducted on some benchmark models show a significant reduction in the size of the reduced models as compared to those obtained through conventional procedures.

Keywords: large systems; model order reduction; MOR; iterative; Krylov subspace; moments; singular values; numerical rank; large system dynamics; stopping criterion; order selection automation.

DOI: 10.1504/IJMIC.2013.053538

International Journal of Modelling, Identification and Control, 2013 Vol.18 No.4, pp.332 - 340

Published online: 29 Apr 2013 *

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