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A fully adaptive rational global Arnoldi method for the model-order reduction of second-order MIMO systems with proportional damping

Author

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  • Bonin, Thomas
  • Faßbender, Heike
  • Soppa, Andreas
  • Zaeh, Michael

Abstract

The model order reduction of second-order dynamical multi-input and multi-output (MIMO) systems with proportional damping arising in the numerical simulation of mechanical structures is discussed. Based on finite element modelling the systems describing the mechanical structures are large and sparse, either undamped or proportionally damped. This work concentrates on a new model reduction algorithm for such second order MIMO systems which automatically generates a reduced system approximating the transfer function in the lower range of frequencies. The method is based on the rational global Arnoldi method. It determines the expansion points iteratively. The reduced order and the number of moments matched per expansion point are determined adaptively using a heuristic based on some error estimation. Numerical examples comparing our results to modal reduction and reduction via the rational block Arnoldi method are presented.

Suggested Citation

  • Bonin, Thomas & Faßbender, Heike & Soppa, Andreas & Zaeh, Michael, 2016. "A fully adaptive rational global Arnoldi method for the model-order reduction of second-order MIMO systems with proportional damping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 1-19.
    • Handle: RePEc:eee:matcom:v:122:y:2016:i:c:p:1-19
    DOI: 10.1016/j.matcom.2015.08.017
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    References listed on IDEAS

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    1. Chu, Chia-Chi & Lai, Ming-Hong & Feng, Wu-Shiung, 2008. "Model-order reductions for MIMO systems using global Krylov subspace methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1153-1164.
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    Cited by:

    1. Li, Yanpeng & Jiang, Yaolin & Yang, Ping, 2021. "Time domain model order reduction of discrete-time bilinear systems with Charlier polynomials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 905-920.
    2. Wang, Zhao-Hong & Jiang, Yao-Lin & Xu, Kang-Li, 2023. "Reduced-order state-space models for two-dimensional discrete systems via bivariate discrete orthogonal polynomials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 441-456.

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