Asymptotic Analysis for Different Partitionings of RLC Transmission Lines

Gander, Martin J.; Kumbhar, Pratik M.; Ruehli, Albert E.

doi:10.1007/978-3-030-56750-7_28

Cited by 3 publications

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“…There are also analyses at the discrete level for OWR applied to RC circuits [34]. WR and OWR were also studied for RLCG transmission lines [1,15,16,20,11]. A different approach for the interconnect circuits has been studied in [27], where the interconnect circuit is partitioned using Norton interfaces which depend upon resistors.…”

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Analysis of Overlap in Waveform Relaxation Methods for RC Circuits

Gander

Kumbhar

Ruehli

2018

Lecture Notes in Computational Science and Engineering

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Waveform relaxation (WR) methods are based on partitioning large circuits into sub-circuits which then are solved separately for multiple time steps in so 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.

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