ℋ_2 optimal structure-preserving model order reduction of second-order systems by iterative rational Krylov algorithm

06/24/2020
by   Md. Motlubar Rahman, et al.
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In this paper, we focus on the efficient techniques to estimate the ℋ_2 optimal Structure-Preserving Model Order Reduction (SPMOR) of the second-order systems using the Iterative Rational Krylov Algorithm (IRKA). In general, the classical IRKA can be applied to the second-order system by converting it into an equivalent first-order form and get the reduced model in a first-order form. In this case, the reduced model can not preserve the structure of the second-order system which is however necessary for further manipulation. Here we develop IRKA based algorithms that enable us to generate approximate reduced second-order systems without explicitly converting the systems into a first-order form. On the other hand, there are very challenging tasks to find reduced-order form of a large-scale system with a minimized ℋ_2 error norm and attain the rapid rate of convergence. To overcome these problems, this paper discusses competent techniques to determine the optimal ℋ_2 error norm efficiently for the second-order system. The efficiency and applicability of the proposed techniques are validated by applying them to several large-scale dynamical systems. The computation is done numerically and the achieved results are discussed in both tabular and graphical approaches.

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