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Element-Based Model Reduction in Circuit Simulation

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System Reduction for Nanoscale IC Design

Part of the book series: Mathematics in Industry ((MATHINDUSTRY,volume 20))

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Abstract

In this paper, we consider model reduction of linear and nonlinear differential-algebraic equations arising in circuit simulation. Circuit equations obtained using modified nodal or loop analysis have a ;special structure that can be exploited to construct efficient model reduction algorithms. For linear systems, we review passivity-preserving balanced truncation model reduction methods that are based on solving projected Lur’e or Lyapunov matrix equations. Furthermore, a ;topology-based index-preserving procedure for extracting large linear subnetworks from nonlinear circuits is given. Finally, we describe a ;new MATLAB Toolbox PABTEC for model reduction of circuit equations and present some results of numerical experiments.

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Notes

  1. 1.

    http://www.netlib.org/lyapack/.

  2. 2.

    https://www.mpi-magdeburg.mpg.de/projects/mess

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Acknowledgements

The work reported in this paper was supported by the German Federal Ministry of Education and Research (BMBF), grant no. 03STPAE3. Responsibility for the contents of this publication rests with the authors.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, MA 4-5, Straße des 17. Juni 136, 10623, Berlin, Germany

    Andreas Steinbrecher

  2. Institut für Mathematik, Universität Augsburg, Universitätsstraße ;14, 86159, Augsburg, Germany

    Tatjana Stykel

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  1. Andreas Steinbrecher
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  2. Tatjana Stykel
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Correspondence to Tatjana Stykel .

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  1. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

    Peter Benner

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Steinbrecher, A., Stykel, T. (2017). Element-Based Model Reduction in Circuit Simulation. In: Benner, P. (eds) System Reduction for Nanoscale IC Design. Mathematics in Industry, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-07236-4_2

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