Automatic Generation of Reduced-Order Models for Linear Parametric Systems

  • Lihong FengEmail author
  • Athanasios C. Antoulas
  • Peter Benner
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 22)


Parametric modeling as well as parametric model order reduction (PMOR) of parametric systems are being widely researched in many micro- and nano-electrical(-mechanical) problems as well as in coupled micro- and nano-electro-thermal problems. We propose an adaptive technique for automatically implementing PMOR, so as to automatically construct the reduced-order models. The adaptive technique is based on a posteriori error estimation and is realized through a greedy algorithm which uses the error estimation as a stopping criteria.


Model order reduction Multi-moment-matching Parametric model order reduction 



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.


  1. 1.
    Baur, U., Benner, P., Beattie, C., Gugercin, S.: Interpolatory projection methods for parameterized model reduction. SIAM J. Sci. Comput. 33, 2489–2518 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bechtold, T., Hohlfeld, D., Rudnyi, E.B., Guenther, M.: Efficient extraction of thin-film thermal parameters from numerical models via parametric model order reduction. J. Micromech. Microeng. 20, 045030 (2010)CrossRefGoogle Scholar
  3. 3.
    Benner, P., Feng, L.: A robust algorithm for parametric model order reduction based on implicit moment-matching. In: Quarteroni, G.R.A. (ed.) Reduced Order Methods for Modeling and Computational Reduction. MS&A, vol. 9, pp. 159–186. Springer, Cham (2014)Google Scholar
  4. 4.
    Bui-Thanh, T., Willcox, K., Ghattas, O.: Model reduction for large-scale systems with high-dimensional parametric input space. SIAM J. Sci. Comput. 30, 3270–3288 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Feng, L., Benner, P., Antoulas, A. C.: An a posteriori error bound for reduced order modeling of micro-and nano-electrical (-mechanical) systems. In: SCEE-2014 (Scientific Computing in Electrical Engineering), Wuppertal, Germany (2014)Google Scholar
  6. 6.
    Lefteriu, S., Antoulas, A.C., Ionita, A.C.: Parametric model reduction in the Loewner framework. In: Proceedings of 18th IFAC World Congress, pp. 12752–12756 (2011)Google Scholar
  7. 7.
    Patera, A.T., Rozza, G.: Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations. MIT Pappalardo Graduate Monographs in Mechanical Engineering, Version 1.0, Copyright MIT 2006 (2007)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Lihong Feng
    • 1
    Email author
  • Athanasios C. Antoulas
    • 2
  • Peter Benner
    • 1
  1. 1.Max Planck Institute for Dynamics of Complex Technical Systems39106 MagdeburgGermany
  2. 2.Department of Electrical and Computer EngineeringRice UniversityTXUSA

Personalised recommendations