Skip to main content
SpringerLink
Log in

Analysis of Overlap in Waveform Relaxation Methods for RC Circuits

  • Conference paper
  • First Online:
Domain Decomposition Methods in Science and Engineering XXIV (DD 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

Included in the following conference series:

Abstract

Waveform relaxation (WR) methods are based on partitioning large circuits into sub-circuits which can be solved separately, and an iteration using transmission conditions then leads to better and better approximations of the entire circuit. Optimized waveform relaxation (OWR) methods work similarly, but they use more effective transmission conditions between sub-circuits. We study here for the first time the influence of overlap on WR and OWR applied to RC circuits. We derive an optimization problem which characterizes the best choice of certain resistance parameters in the transmission conditions for convergence, and give an asymptotic solution of this optimization problem. We also illustrate our results with numerical experiments.

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

Access this chapter

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 EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
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

References

  1. M.D. Al-Khaleel, M.J. Gander, A.E. Ruehli, Optimization of transmission conditions in waveform relaxation techniques for RC circuits. SIAM J. Numer. Anal. 52(2), 1076–1101 (2014)

    Article  MathSciNet  Google Scholar 

  2. M.J. Gander, P.M. Kumbhar, Asymptotic analysis of optimized waveform relaxation methods for RC type circuits (2018, in preparation)

    Google Scholar 

  3. M.J. Gander, A.E. Ruehli, Optimized waveform relaxation methods for RC type circuits. IEEE Trans. Circuits Syst. I Regul. Pap. 51(4), 755–768 (2004)

    Article  MathSciNet  Google Scholar 

  4. C.W. Ho, A. Ruehli, P. Brennan, The modified nodal approach to network analysis. IEEE Trans. Circuits Syst. 22(6), 504–509 (1975)

    Article  Google Scholar 

  5. E. Lelarasmee, A.E. Ruehli, A.L. Sangiovanni-Vincentelli, The waveform relaxation method for time-domain analysis of large scale integrated circuits. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 1(3), 131–145 (1982)

    Article  Google Scholar 

  6. T. Menkad, A. Dounavis, Resistive coupling-based waveform relaxation algorithm for analysis of interconnect circuits. IEEE Trans. Circuits Syst. I Regul. Pap. 64(7), 1877–1890 (2017)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Section de Mathématiques, Université de Genève, Geneva, Switzerland

    Martin J. Gander & Pratik M. Kumbhar

  2. EMC Laboratory, Missouri University of Science and Technology, Rolla, MO, USA

    Albert E. Ruehli

Authors
  1. Martin J. Gander
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pratik M. Kumbhar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Albert E. Ruehli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Martin J. Gander , Pratik M. Kumbhar or Albert E. Ruehli .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Louisana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

  3. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

    Lawrence Halpern

  4. Department of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Ralf Kornhuber

  6. Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

  7. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    Olof B. Widlund

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Gander, M.J., Kumbhar, P.M., Ruehli, A.E. (2018). Analysis of Overlap in Waveform Relaxation Methods for RC Circuits. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_26

Download citation

Publish with us

Policies and ethics

Search

Navigation