TY - JOUR
T1 - Optimized waveform relaxation methods for RC circuits
T2 - Discrete case
AU - Wu, Shu Lin
AU - Al-Khaleel, Mohammad D.
N1 - Funding Information:
The authors are very grateful to the anonymous referees for the careful reading of a preliminary version of the manuscript and their valuable suggestions and comments, which greatly improved the quality of this paper. The authors are also very grateful to Professor Annalisa Buffa as the editor of this paper for handling the submission and review of this paper. This work is supported by the NSF of China (11301362, 11371157, 11671074, 61573010), the NSF of Technology & Education of Sichuan Province (2014JQ0035, 15ZA0220), the China Postdoctoral Foundation (2015M580777, 2016T90841) and the project of Sichuan University of Science and Engineering (2015LX01).
Publisher Copyright:
© EDP Sciences, SMAI 2016.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - 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 α opt c from the continuous analysis, we show that the convergence rates can be further improved by using the one αdopt α opt d analyzed at the discrete level, while for the Trapezoidal rule, it is better to use αcopt α opt c. This conclusion is confirmed by numerical results.
AB - 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 α opt c from the continuous analysis, we show that the convergence rates can be further improved by using the one αdopt α opt d analyzed at the discrete level, while for the Trapezoidal rule, it is better to use αcopt α opt c. This conclusion is confirmed by numerical results.
KW - Discretization
KW - Parameter optimization
KW - RC circuits
KW - Waveform relaxation (WR)
UR - http://www.scopus.com/inward/record.url?scp=84999886490&partnerID=8YFLogxK
U2 - 10.1051/m2an/2016061
DO - 10.1051/m2an/2016061
M3 - Article
AN - SCOPUS:84999886490
SN - 2822-7840
VL - 51
SP - 209
EP - 223
JO - ESAIM: Mathematical Modelling and Numerical Analysis
JF - ESAIM: Mathematical Modelling and Numerical Analysis
IS - 1
ER -