Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Applied Parallel Computing

PARA 2004: Applied Parallel Computing. State of the Art in Scientific Computing pp 323–332Cite as

Structure-Preserving Model Reduction

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3732))

Abstract

A general framework for structure-preserving model reduction by Krylov subspace projection methods is developed. The goal is to preserve any substructures of importance in the matrices L, G, C, B that define the model prescribed by transfer function H(s)=L *(G +sC)− − 1 B. Many existing structure-preserving model-order reduction methods for linear and second-order dynamical systems can be derived under this general framework.

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

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 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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Antoulas, A.C., Sorensen, D.C., Gugercin, S.: A survey of model reduction methods for large-scale systems. In: Olshevsky, V. (ed.) Structured Matrices in Mathematics, Computer Science, and Engineering I: Proceedings of an AMS-IMS-SIAM joint summer research conference, University of Co0lorado, Boulder, June 27-July 1, 1999. Comtemporary Mathematics, vol. 280, pp. 193–219. American Mathematical Society, Providence (2001)

    Google Scholar 

  2. Bai, Z.: Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Applied Numerical Mathematics 43, 9–44 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bai, Z., Su, Y.: SOAR: A second-order Arnoldi method for the solution of the quadratic eigenvalue problem. Computer Science Technical Report CSE-2003-21, University of California, Davis, California, SIAM J. Matrix Anal. Appl. 26(3), 640–659 (2003)

    Google Scholar 

  4. Bai, Z., Su, Y.: Dimension reduction of second-order dynamical systems via a second-order Arnoldi method. Computer Science Technical Report CSE-2004-1, University of California, Davis, California, SIAM J. Sci. Comp. 26(5), 1692–1709 (2004)

    Google Scholar 

  5. Freund, R.: Pade-type reduced-order modeling of higher-order systems. Presentation at Oberwolfach Mini-Workshop on Dimensional Reduction of Large-Scale Systems (October 2003)

    Google Scholar 

  6. Freund, R.W., Feldmann, P.: The SyMPVL algorithm and its applications to interconnect simulation. In: Proc. 1997 InternationalConference on Simulation of SemiconductorProcesses and Devices, Piscataway, New Jersey, pp. 113–116. IEEE, Los Alamitos (1997)

    Google Scholar 

  7. Freund, R.W.: Model reduction methods based on Krylov subspaces. Acta Numerica 12, 267–319 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Grimme, E.J.: Krylov Projection Methods For Model Reduction. PhD thesis, University of Illinois at Urbana-Champaign, Urbana, Illinois (1997)

    Google Scholar 

  9. Hoffnung, L.: Subspace Projection Methods for the Quadratic Eigenvalue Problem. PhD thesis, University of Kentucky, Lexington, KY (August 2004)

    Google Scholar 

  10. Li, R.-C., Bai, Z.: Structure-preserving model reductions using a Krylov subspace projection formulation. Technical Report CSE-2004-24, Department of Computer Science, University of California, Davis, Comm. Math. Sci. 3(2), 179–199 (2004)

    Google Scholar 

  11. Meyer, D.G., Srinivasan, S.: Balancing and model reduction for second-order form linear systems. IEEE Transactions on Automatic Control 41(11), 1632–1644 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. Odabasioglu, A., Celik, M., Pileggi, L.T.: PRIMA: passive reduced-order interconnect macromodeling algorithm. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 17(8), 645–654 (1998)

    Article  Google Scholar 

  13. Ruhe, A.: Rational Krylov sequence methods for eigenvalue computation. Linear Algebra and Its Applications 58, 391–405 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  14. Ruhe, A.: Rational Krylov algorithms for nonsymmetric eigenvalue problems. ii. matrix pairs. Linear Algebra and Its Applications 197-198, 283–295 (1994)

    Article  MathSciNet  Google Scholar 

  15. Salimbahrami, B., Lohmann, B.: Structure preserving order reduction of large scale second order systems. In: Proceeding of 10th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory and Applications, Osaka, Japan, July 2004, pp. 245–250 (2004)

    Google Scholar 

  16. Slone, R.D.: A computationally efficient method for solving electromagnetic interconnect problems: the Padé approximation via the Lanczos process with an error bound. Master’s thesis, University of Kentucky, Lexington, KY (1997)

    Google Scholar 

  17. Su, T.-J., Craig, R.R.: Model reduction and control of flexible structures using Krylov vectors. J. Guidance, Control, and Dynamics 14(2), 260–267 (1991)

    Article  Google Scholar 

  18. Vandendorpe, A., Van Dooren, P.: Krylov techniques for model reduction of second-order systems. Unpublished Note, March 2 (2004)

    Google Scholar 

  19. Villemagne, C.E., Skelton, R.E.: Model reduction using a projection formulation. Int. J. Control 46(6), 2141–2169 (1987)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington, KY, 40506, USA

    Ren-Cang Li

  2. Department of Computer Science and Department of Mathematics, University of California, Davis, CA, 95616, USA

    Zhaojun Bai

Authors
  1. Ren-Cang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhaojun Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Science Department, University of Tennessee, 37996-3450, Knoxville, TN, USA

    Jack Dongarra

  2. Department of Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Kaj Madsen

  3. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Li, RC., Bai, Z. (2006). Structure-Preserving Model Reduction. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_38

Download citation

  • DOI: https://doi.org/10.1007/11558958_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29067-4

  • Online ISBN: 978-3-540-33498-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation