OPTIMIZED WAVEFORM RELAXATION METHODS FOR RC CIRCUITS: DISCRETE CASE
OPTIMIZED WAVEFORM RELAXATION METHODS FOR RC CIRCUITS: DISCRETE CASE
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RC 电路的优化波形弛豫方法：离散情况
DOI：
10.1051/m2an/2016061
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Mohammad D. Al-Khaleel
中科院分区：
文献类型：
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作者：
Shu-Lin Wu;Mohammad D. Al-Khaleel
优化波形松弛（OWR）方法得益于子系统之间的智能信息交换，即所谓的传输条件（TCs），近年来被认为是大规模电路的有效求解方法，受到了广泛的关注。TCs包含一个自由参数α，该参数对收敛速度有重要影响。到目前为止，寻找最佳参数的分析仅仅是在连续水平上进行的，这种分析没有考虑到时间离散化的影响。在本文中，我们证明了时间离散化确实对wr方法有重要影响。精确地说，对于后向欧拉方法，与连续分析的αc opt参数相比，在离散水平上使用一个αd opt可以进一步提高收敛速度，而对于梯形规则，使用αc opt更好，数值结果证实了这一结论。
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 αc opt from the continuous analysis, we show that the convergence rates can be further improved by using the one αd opt analyzed at the discrete level, while for the Trapezoidal rule, it is better to use αc opt. This conclusion is confirmed by numerical results.