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A framework for parametric reduction in large-scale nonlinear dynamical systems

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Abstract

This manuscript presents a general parametric model order reduction (pMOR) framework for nonlinear dynamical systems. At first, a family of local nonlinear reduced order models (ROMs) is generated for different parametric space vectors using the nonlinear moment matching (NLMM) scheme along-with the discrete empirical interpolation method (DEIM). Then, the nonlinear reduced order model for any new parameter is obtained by interpolating the neighbouring reduced order models after projecting them onto a universal subspace. The advantage of such a scheme is that the parametric dependency is maintained in the reduced nonlinear models. Finally, we substantiate our observations by a suite of numerical tests.

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Acknowledgements

The Doctoral fellowship of Author 1 from Ministry of Human Resource Development (MHRD), New Delhi, India, via Grant No. (2017PHAELE006) is duly acknowledged. Authors would like to thank Maria Cruz Varona for sharing NLMM code and for fruitful discussions. Authors would also like to thank the anonymous reviewers for their expert advice in improving the quality of this manuscript.

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  1. Department of Electrical Engineering, National Institute of Technology, Srinagar, 190006, India

    Danish Rafiq & Mohammad Abid Bazaz

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  1. Danish Rafiq
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Correspondence to Danish Rafiq.

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Rafiq, D., Bazaz, M.A. A framework for parametric reduction in large-scale nonlinear dynamical systems. Nonlinear Dyn 102, 1897–1908 (2020). https://doi.org/10.1007/s11071-020-05970-3

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