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Parametric and Reduced-Order Modeling for the Thermal Analysis of Nanoelectronic Structures

  • Lihong FengEmail author
  • Peter Meuris
  • Wim Schoenmaker
  • Peter Benner
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 23)

Abstract

In this work, we discuss the parametric modeling for the thermodynamic analysis of components of nanoelectronic structures and automatic model order reduction of the consequent parametric models. Given the system matrices at different values of the parameters, we introduce a simple method of extracting system matrices which are independent of the parameters, so that parametric models of a class of linear parametric problems can be constructed. Then the reduced-order models of the large-scale parametric models are automatically obtained using a posteriori output error bounds for the reduced-order models. A thermal problem with conductance variations is studied as an example to illustrate the proposed parametric modeling and model order reduction techniques.

Notes

Acknowledgements

This work is supported by the collaborative project nanoCOPS, Nanoelectronic COupled Problems Solutions, supported by the European Union in the FP7-ICT-2013-11 Program under Grant Agreement Number 619166.

References

  1. 1.
    Benner, P., Feng, L.: A robust algorithm for parametric model order reduction based on implicit moment matching. In: Quarteroni, A., Rozza, G. (eds.) Springer MS &A Series. Reduced Order Methods for Modeling and Computational Reduction, vol. 8, pp. 159–185. Springer International Publishing, Switzerland (2014)Google Scholar
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    Benner, P., Gugercin, S., Willcox, L.: A survey of model reduction methods for parametric systems. SIAM Review 57(4), 483–531 (2015)MathSciNetCrossRefGoogle Scholar
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    Benner, P., Feng, L., Schoenmaker, W., Meuris, P.: Parametric modeling and model order reduction of coupled problems. ECMI Newsl. 56, 68–69 (2014). Available from http://www.mafy.lut.fi/EcmiNL/issues.php Google Scholar
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    Feng, L., Antoulas, A.C., Benner, P.: Some a posteriori error bounds for reduced order modelling of (non-)parametrized linear systems MPI Magdeburg Preprint MPIMD/15-17, October 2015. Available from: http://www.mpi-magdeburg.mpg.de/preprints/.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Lihong Feng
    • 1
    Email author
  • Peter Meuris
    • 2
  • Wim Schoenmaker
    • 2
  • Peter Benner
    • 3
  1. 1.Max Planck Institute for Dynamics of Complex Technical Systems39106 MagdeburgGermany
  2. 2.Magwel NV3000 LeuvenBelgium
  3. 3.Max Planck Institute for Dynamics of Complex Technical Systems39106 MagdeburgGermany

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