Proceedings chapter

Analysis of Overlap in Waveform Relaxation Methods for RC Circuits

Published inDomain decomposition methods in science and engineering XXIV, Editors Bjørstad, Petter E., p. 281-289
Presented at Svalbard, Norway, February 6 - 10, 2017
PublisherCham : Springer
  • Lecture notes in computational science and engineering; 125
Publication date2018-01-05
First online date2019-01-05

Waveform relaxation (WR) methods are based on partitioning large circuits into sub-circuits which then are solved separately for multiple time steps in co called time windows, and an iteration is used to converge to the global circuit solution in each time window. Classical WR converges quite slowly, especially when long time windows are used. To overcome this issue, optimized WR (OWR) was introduced which is based on optimized transmission conditions that transfer information between the sub-circuits more efficiently than classical WR. We study here for the first time the influence of overlapping sub-circuits in both WR and OWR applied to RC circuits. We give a circuit interpretation of the new transmission conditions in OWR, and derive closed form asymptotic expressions for the circuit elements representing the optimization parameter in OWR. Our analysis shows that the parameter is quite different in the overlapping case, compared to the non-overlapping one. We then show numerically that our optimized choice performs well, also for cases not covered by our analysis. This paper provides a general methodology to derive optimized parameters and can be extended to other circuits or system of differential equations or space-time PDEs.

  • Optimized Waveform Relaxation
  • RC circuits
  • Asymptotic Analysis
Citation (ISO format)
GANDER, Martin Jakob, KUMBHAR, Pratik Mahadeo, RUEHLI, Albert E. Analysis of Overlap in Waveform Relaxation Methods for RC Circuits. In: Domain decomposition methods in science and engineering XXIV. Svalbard, Norway. Cham : Springer, 2018. p. 281–289. (Lecture notes in computational science and engineering) doi: 10.1007/978-3-319-93873-8_26
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Proceedings chapter (Accepted version)

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