Skip to main content

Model Order Reduction for Nonlinear IC Models with POD

  • Conference paper
  • First Online:
Scientific Computing in Electrical Engineering SCEE 2008

Part of the book series: Mathematics in Industry ((TECMI,volume 14))

Abstract

Due to refined modelling of semiconductor devices and increasing packing densities, reduced order modelling of large nonlinear systems is of great importance in the design of integrated circuits (ICs). Despite the linear case, methodologies for nonlinear problems are only beginning to develop. The most practical approaches rely either on linearisation, making techniques from linear model order reduction applicable, or on proper orthogonal decomposition (POD), preserving the nonlinear characteristic. In this paper we focus on POD. We demonstrate the missing point estimation and propose a new adaption of POD to reduce both dimension of the problem under consideration and cost for evaluating the full nonlinear system.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Antoulas, A.C.: Approximation of Large-Scale Dynamical Systems. SIAM (2005)

    Google Scholar 

  2. Scherpen, J.M.A.: Balancing for nonlinear systems. Ph.D. thesis, University of Twente (1994)

    Google Scholar 

  3. Ionescu, T.C., Scherpen, J.M.A.: Positive Real Balancing for Nonlinear Systems. In: G. Ciuprina, D. Ioan (eds.) Scientific Computing in Electrical Engineering – SCEE 2006, Mathematics in Industry, vol. 11, pp. 153–159. The European Consortium for Mathematics in Industry, Springer-Verlag Berlin Heidelberg (2007)

    Chapter  Google Scholar 

  4. Rewieński, M.J., White, J.: A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices. IEEE Trans. CAD Int. Circ. Syst. 22(2), 155–170 (2003)

    Article  Google Scholar 

  5. Voß, T., Pulch, R., ter Maten, J., El Guennouni, A.: Trajector piecewise linear aproach for nonlinear differential-algebraic equations in circuit simulation. In: G. Ciuprina, D. Ioan (eds.) Scientific Computing in Electrical Engineering – SCEE 2006, pp. 167–173. Springer (2007)

    Google Scholar 

  6. Holmes, P., Lumley, J., Berkooz, G.: Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambrige University Press, Cambrige, UK (1996)

    Book  MATH  Google Scholar 

  7. Loève, M.: Probability Theory. Van Nostrand (1955)

    Google Scholar 

  8. Rathinam, M., Petzold, L.R.: A new look at proper orthogonal decomposition. SIAM J. Numer. Anal. 41(5), 1893–1925 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Pinnau, R.: Model reduction via proper orthogonal decomposition. In: W. Schilders, H. van der Vorst, J. Rommes (eds.) Model order reduction: theory, applications, and research aspects, pp. 95–109. Springer (2008)

    Google Scholar 

  10. Willcox, K., Peraire, J.: Balanced model reduction via the proper orthogonal decomposition. AIAA Journal 40(11), 2323–2330 (2002)

    Article  Google Scholar 

  11. Astrid, P.: Reduction of process simulation models: a proper orthogonal decomposition approach. Ph.D. thesis, Technische Universiteit Eindhoven (2004)

    Google Scholar 

  12. Astrid, P., Verhoeven, A.: Application of least squares mpe technique in the reduced order modeling of electrical circuits. In: Proceedings of the 17th Int. Symp. MTNS, pp. 1980–1986 (2006)

    Google Scholar 

  13. Astrid, P., Weiland, S.: On the construction of pod models from partial observations. In: Proceedings of the 44rd IEEE Conference on Decision and Control, pp. 2272–2277 (2005)

    Google Scholar 

  14. Verhoeven, A.: Redundancy reduction of ic models by multirate time-integration and model order reduction. Ph.D. thesis, Technische Universiteit Eindhoven (2008)

    Google Scholar 

  15. Rewieński, M.J.: A trajectory piecewise-linear approach to model order reduction of nonlinear dynamical systems. Ph.D. thesis, Massachusetts Institute of Technology (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Arie Verhoeven .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Verhoeven, A., Striebel, M., ter Maten, E.J.W. (2010). Model Order Reduction for Nonlinear IC Models with POD. In: Roos, J., Costa, L. (eds) Scientific Computing in Electrical Engineering SCEE 2008. Mathematics in Industry(), vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12294-1_70

Download citation

Publish with us

Policies and ethics