A new relaxation algorithm for circuit simulation that combines the advantages of iterated timing analysis (ITA) and waveform relaxation (WR) is described. The method is based on using an iterative stepsize refinement strategy with a waveform-relaxation-newton (WRN) algorithm. All three relaxation techniques, ITA, WR, and WRN, are compared, and experimental results that indicate the strengths and weaknesses of the methods are presented. In addition, a new convergence proof for the waveform-Newton (WN) method for systems with nonlinear capacitors is provided. Finally, it is shown that the step-refined WRN algorithm can be implemented on a parallel processor in such a way that different subsystems can be processed in parallel and the solution at different timepoints of the same subsystem can also be computed in parallel.
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