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 , 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.
Accepté le :
DOI : 10.1051/m2an/2016061
Mots clés : Waveform relaxation (WR), discretization, parameter optimization, RC circuits
@article{M2AN_2017__51_1_209_0,
author = {Wu, Shu-Lin and Al-Khaleel, Mohammad D.},
title = {Optimized waveform relaxation methods for {RC} circuits: discrete case},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {209--223},
publisher = {EDP-Sciences},
volume = {51},
number = {1},
year = {2017},
doi = {10.1051/m2an/2016061},
zbl = {1364.65138},
mrnumber = {3601007},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2016061/}
}
TY - JOUR AU - Wu, Shu-Lin AU - Al-Khaleel, Mohammad D. TI - Optimized waveform relaxation methods for RC circuits: discrete case JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 209 EP - 223 VL - 51 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016061/ DO - 10.1051/m2an/2016061 LA - en ID - M2AN_2017__51_1_209_0 ER -
%0 Journal Article %A Wu, Shu-Lin %A Al-Khaleel, Mohammad D. %T Optimized waveform relaxation methods for RC circuits: discrete case %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 209-223 %V 51 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016061/ %R 10.1051/m2an/2016061 %G en %F M2AN_2017__51_1_209_0
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. http://www.numdam.org/articles/10.1051/m2an/2016061/
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