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/
M. Al-Khaleel, Optimized waveform relaxation methods for circuit simulations. Ph.D. dissertation, McGill University (2007). | MR
M.D. Al-Khaleel, M.J. Gander and A.E. Ruehli, Optimized waveform relaxation solution of RLCG transmission line type circuits, In IEEE 9th International Conference on Innovations in Information Technology (IIT). IEEE Publisher (2013) 136–140.
, and , A mathematical analysis of optimized waveform relaxation for a small RC circuit. Appl. Numer. Math. 75 (2014) 61–76. | DOI | MR | Zbl
, and , Optimization of transmission conditions in waveform relaxation techniques for RC circuits. SIAM J. Numer. Anal. 52 (2014) 1076–1101. | DOI | MR | Zbl
and , Optimized waveform relaxation methods for RC type circuits. IEEE Trans. Circuits Syst. I, Reg. Papers 51 (2004) 755–768. | DOI | MR | Zbl
and , Space-Time continuous analysis of waveform relaxation for the heat equation. SIAM J. Sci. Comput. 19 (1998) 2014–2031. | DOI | MR | Zbl
and , Méthodes de relaxation d’ondes pour l’équation de la chaleur en dimension 1. C.R. Acad. Sci. Paris, Série I 336 (2003) 519–524. | DOI | MR | Zbl
and , Optimized Schwarz waveform relaxation for advection reaction diffusion problems. SIAM J. Numer. Anal. 45 (2007) 666–697. | DOI | MR | Zbl
M.J. Gander, M. Al-Khaleel and A.E. Ruehli, Waveform relaxation technique for longitudinal partitioning of transmission lines, in Digest of Electr. Perf. Electronic Packaging (2006), pp. 207–210.
, and , Optimal Schwarz waveform relaxation for the one dimensional wave equation. SIAM J. Numer. Anal. 41 (2003) 1643–1681. | DOI | MR | Zbl
M.J. Gander and A.E. Ruehli, Optimized waveform relaxation solution of electromagnetic and circuit problems. IEEE 19th Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS) (2010) 65–68.
, and , Optimized waveform relaxation methods for longitudinal partitioning of transmission lines. IEEE Trans. Circuits Syst. I Reg. Papers 56 (2009) 1732–1743. | DOI | MR | Zbl
and , Space-time domain decomposition for parabolic problems. Numer. Math. 93 (2002) 279–313. | DOI | MR | Zbl
, On time-domain simulation of lossless transmission lines with nonlinear terminations. SIAM J. Numer. Anal. 42 (2004) 1018–1031. | DOI | MR | Zbl
E. Lelarasmee, A.E. Ruehli and A.L. Sangiovanni-Vincentelli, The waveform relaxation methods for time-domain analysis of large scale integrated circuits. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. CAD-1 (1982) 131–145.
, Remarks on Picard-Lindelöf iterations, Part I. BIT Numer. Math. 29 (1989) 328–346. | DOI | MR | Zbl
A.E. Ruehli and T.A. Johnson, Circuit analysis computing by waveform relaxation, in Wiley Encyclopedia of Electrical Electronics Engineering. Wiley, New York (1999).
J.C. Strikwerda, Finite difference schemes and partial differential equations. Chapman and Hall (1989). | MR | Zbl
Cité par Sources :
