Analysis of Overlap in Waveform Relaxation Methods for RC Circuits

  • Martin J. GanderEmail author
  • Pratik M. KumbharEmail author
  • Albert E. RuehliEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 125)


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.


  1. 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)MathSciNetCrossRefGoogle Scholar
  2. 2.
    M.J. Gander, P.M. Kumbhar, Asymptotic analysis of optimized waveform relaxation methods for RC type circuits (2018, in preparation)Google Scholar
  3. 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)MathSciNetCrossRefGoogle Scholar
  4. 4.
    C.W. Ho, A. Ruehli, P. Brennan, The modified nodal approach to network analysis. IEEE Trans. Circuits Syst. 22(6), 504–509 (1975)CrossRefGoogle Scholar
  5. 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)CrossRefGoogle Scholar
  6. 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)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Section de MathématiquesUniversité de GenèveGenevaSwitzerland
  2. 2.EMC LaboratoryMissouri University of Science and TechnologyRollaUSA

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