Skip to main content

Model Order Reduction of Nonlinear Systems in Circuit Simulation: Status and Applications

  • Chapter
  • First Online:
Model Reduction for Circuit Simulation

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 74))

Abstract

In this paper we review the status of existing techniques for nonlinear model order reduction by investigating how well these techniques perform for typical industrial needs. In particular the Trajectory Piecewise Linear-method and the Proper Orthogonal Decomposion approach are taken under consideration.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Notes

  1. 1.

    Most frequently \(\mathbf{V}\) is constructed to be orthogonal, such that \(\mathbf{W}=\mathbf{V}\) can be chosen.

  2. 2.

    Similar results are obtained from a matlab-implementation using ode15s as integration scheme.

  3. 3.

    The models used arise from linearization around the states the system was in during training at \(t\in \{0.0, 3.01943, 3.04244\}\).

References

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

    Book  MATH  Google Scholar 

  2. Astrid, P., Weiland, S., Willcox, K., Backx, T.: Missing point estimation in models described by proper orthogonal decomposition. IEEE Trans. Automat. Contr. 53(10), 2237–2251 (2008)

    Article  MathSciNet  Google Scholar 

  3. Benner, P., Damm, T.: Lyapunov equations, energy functionals and model order reduction. Submitted for publication

    Google Scholar 

  4. Chaturantabut, C., Sorensen, D.C., Rice, U.: Discrete empirical interpolation for nonlinear model reduction. Tech. Rep. TR09–05, CAAM (2009)

    Google Scholar 

  5. Condon, M., Ivanov, R.: Nonlinear systems—algebraic gramians and model reduction. COMPEL: Int J Comput Mathe Elect Electron Eng 24(1), 202–219 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Condon, M., Ivanov, R.: Krylov subspaces from bilinear representations of nonlinear systems. COMPEL: Int. J. Comput. Math. Electr. Electron. Eng. 26(2), 399–406 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Freund, R.W.: Krylov-subspace methods for reduced-order modeling in circuit simulation. J. Comput. Appl. Math. 123(1–2), 395–421 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Fujimoto, K., Scherpen, J.M.A.: Singular value analysis and balanced realizations for nonlinear systems. In: Schilders, W.H.A., van der Vorst, H.A., Rommes, J. (eds.) Model Order Reduction: Theory, Research Aspects and Applications. pp. 251–272 Springer, Berlin (2008)

    Chapter  Google Scholar 

  9. Gad, E., Nakhla, M.: Efficient model reduction of linear periodically time-varying systems via compressed transient system function. IEEE Trans. Circ. Syst. 52(6), 1188–1204 (2005)

    Article  MathSciNet  Google Scholar 

  10. Grepl, M., Maday, Y., Nguyen, N., Patera, A.: Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. Math. Model. Numer. Anal. 41(3), 575–605 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Günther, M.: Simulating digital circuits numerically—a charge-oriented ROW approach. Numer. Math. 79, 203–212 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Holmes, P., Lumley, J.L., Berkooz, G.: Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge Monographs on Mechanics. Cambridge University Press, Cambridge (1996)

    Book  Google Scholar 

  13. Moore, B.: Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Automat. Contr. 26(1), 17–32 (1981)

    Article  MATH  Google Scholar 

  14. Pinnau, R.: Model reduction via proper orthogonal decomposition. In: Schilders, W., van der Vorst, H., Rommes, J. (eds.) Model Order Reduction: Theory, Applications, and Research Aspects, pp. 95–109. Springer, Berlin (2008)

    Chapter  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 

  16. Sirovich, L.: Turbulence and the dynamics of coherent structures part I-III. Q. App. Math. 45(3), 561–571, 573–590 (1987)

    Google Scholar 

  17. Striebel, M., Bartel, A., Günter, M.: A multirate ROW-scheme for index-1 network equations. Appl. Numer. Math. 59(3–4), 800–814 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  18. Striebel, M., Rommes, J.: Model order reduction of nonlinear systems in circuit simulation: status, open issues, and applications. CSC Preprint 08-07, Chemnitz University of Technology, http://www.tu-chemnitz.de/mathematik/csc/index.php (2008)

    Google Scholar 

  19. Verhoeven, A., ter Maten, J., Striebel, M., Mattheij, R.: Model order reduction for nonlinear IC models. CASA-Report 07–41, TU Eindhoven (2007). To appear in IFIP2007 conference proceedings

    Google Scholar 

  20. Verriest, E.I.: Time variant balancing and nonlinear balanced realizations. In: Schilders, W.H.A., van der Vorst, H.A., Rommes, J. (eds.) Model Order Reduction: Theory, Research Aspects and Applications. pp. 243–250 Springer Berlin (2008)

    Google Scholar 

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

    Google Scholar 

Download references

Acknowledgements

The work presented is funded by the Marie-Curie Transfer-of-Knowledge project O-MOORE-NICE! under call Identifier FP6-2005-Mobility-3.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael Striebel .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Striebel, M., Rommes, J. (2011). Model Order Reduction of Nonlinear Systems in Circuit Simulation: Status and Applications. In: Benner, P., Hinze, M., ter Maten, E. (eds) Model Reduction for Circuit Simulation. Lecture Notes in Electrical Engineering, vol 74. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0089-5_17

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-0089-5_17

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-0088-8

  • Online ISBN: 978-94-007-0089-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics