Waveform relaxation (WR) methods are based on partitioning large circuits into sub-circuits which then are solved separately for multiple time steps in so called time windows, and an iteration is used to converge to the global circuit solution in each time window. Classical WR converges quite slowly, especially when long time windows are used. To overcome this issue, optimized WR (OWR) was introduced which is based on optimized transmission conditions that transfer information between the sub-circuits more efficiently than classical WR. We study here for the first time the influence of overlapping sub-circuits in both WR and OWR applied to RC circuits. We give a circuit interpretation of the new transmission conditions in OWR, and derive closed form asymptotic expressions for the circuit elements representing the optimization parameter in OWR. Our analysis shows that the parameter is quite different in the overlapping case, compared to the non-overlapping one. We then show numerically that our optimized choice performs well, also for cases not covered by our analysis. This paper provides a general methodology to derive optimized parameters and can be extended to other circuits or system of differential equations or space–time PDEs.

波形松弛（WR）方法基于将大型电路划分为多个子电路，然后分别在所谓的时间窗口中针对多个时间步进行求解，然后使用迭代方法收敛到每个时间窗口中的全局电路解决方案。经典WR收敛非常慢，尤其是在使用长时间窗口的情况下。为了克服这个问题，引入了优化的WR（OWR），它基于优化的传输条件，该条件比传统WR更有效地在子电路之间传输信息。我们第一次在这里研究WR和OWR中重叠子电路应用于RC电路的影响。我们对OWR中的新传输条件进行电路解释，并为代表OWR中最优化参数的电路元件得出闭合形式的渐近表达式。我们的分析表明，与不重叠的情况相比，重叠情况下的参数有很大不同。然后，我们通过数字表明，对于我们的分析未涵盖的情况，我们的优化选择效果良好。本文提供了一种导出优化参数的通用方法，可以扩展到其他电路或系统的微分方程或时空PDE。