Geodesic
Optimized waveform relaxation methods for RC circuits: discrete case
Wu, Shu-Lin1 ; Al-Khaleel, Mohammad D.2, 3
1 Sichuan University of Science and Engineering, Zigong, Sichuan 643000, P.R. China.
2 Department of Mathematics, Yarmouk University, 21163 Irbid, Jordan.
3 Department of Mathematics and Sciences, Khalifa University, 127788 Abu Dhabi, UAE.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 209-223

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The optimized waveform relaxation (OWR) methods, benefiting from intelligent information exchange between subsystems – the so-called transmission conditions (TCs), are recognized as efficient solvers for large scale circuits and get a lot of attention in recent years. The TCs contain a free parameter, namely α, which has a significant influence on the convergence rates. So far, the analysis of finding the best parameter is merely performed at the continuous level and such an analysis does not take into account the influence of temporal discretizations. In this paper, we show that the temporal discretizations do have an important effect on the OWR methods. Precisely, for the Backward–Euler method, compared to the parameter αcopt from the continuous analysis, we show that the convergence rates can be further improved by using the one αdopt analyzed at the discrete level, while for the Trapezoidal rule, it is better to use αcopt. This conclusion is confirmed by numerical results.

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DOI : 10.1051/m2an/2016061
Classification : 65L12, 65L20, 65B99
Keywords: Waveform relaxation (WR), discretization, parameter optimization, RC circuits

Wu, Shu-Lin 1 ; Al-Khaleel, Mohammad D. 2, 3

1 Sichuan University of Science and Engineering, Zigong, Sichuan 643000, P.R. China.
2 Department of Mathematics, Yarmouk University, 21163 Irbid, Jordan.
3 Department of Mathematics and Sciences, Khalifa University, 127788 Abu Dhabi, UAE. 
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     title = {Optimized waveform relaxation methods for {RC} circuits: discrete case},
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     pages = {209--223},
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Wu, Shu-Lin; Al-Khaleel, Mohammad D. Optimized waveform relaxation methods for RC circuits: discrete case. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 209-223. doi: 10.1051/m2an/2016061

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