2020/01/14 by Martin J. Gander, Gander, Martin J., Pratik M. Kumbhar +3 · 1 citation
Computer Science · Engineering · Mathematics · #47N70 #65L05 #65M22 #65N55 #Digital Filter Design and Implementation #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2001.04949
openalex publication_date 2020/01/14 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Waveform relaxation (WR) methods are based on partitioning large circuits\ninto sub-circuits which then are solved separately for multiple time steps in\nso-called time windows, and an iteration is used to converge to the global\ncircuit solution in each time window. Classical WR converges quite slowly,\nespecially when long time windows are used. To overcome this issue, optimized\nWR (OWR) was introduced which is based on optimized transmission conditions\nthat transfer information between the sub-circuits more efficiently than\nclassical WR. We study here for the first time the influence of overlapping\nsub-circuits in both WR and OWR applied to RC circuits. We give a circuit\ninterpretation of the new transmission conditions in OWR and derive closed-form\nasymptotic expressions for the circuit elements representing the optimization\nparameter in OWR. Our analysis shows that the parameter is quite different in\nthe overlapping case, compared to the nonoverlapping one. We then show\nnumerically that our optimized choice performs well, also for cases not covered\nby our analysis. This paper provides a general methodology to derive optimized\nparameters and can be extended to other circuits or system of differential\nequations or space-time PDEs.\n