Abstract

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.

Department(s)

Electrical and Computer Engineering

Comments

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Grant 200020_168999

Keywords and Phrases

Asymptotic analysis; Optimized waveform relaxation; RC circuits

International Standard Serial Number (ISSN)

1573-7691; 0885-7474

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Springer, All rights reserved.

Publication Date

01 Jul 2020

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