Numerical Stability and Multirate Effect in Waveform Relaxation Algorithm with Under Relaxation Technique

Koichi HAYASHI  Hideki ASAI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E75-A    No.6    pp.685-690
Publication Date: 1992/06/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section of Papers Selected from 1991 Joint Technical Conference on Circuits/Systems, Computers and Communications (JTC-CSCC '91))
Category: Combinational/Numerical/Graphic Algorithms
multirate behavior,  waveform relaxation algorithm,  under relaxation technique,  virtual state formulation,  numerical stability,  

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This paper describes the waveform relaxation (WR) algorithm with the under relaxation method based on the virtual state formulation (VSF) technique and the effect of multirate behavior in this algorithm. First, we present the virtual state relaxation method using VSF technique. Next, we introduce the VSF method into WR algorithm in order to exploit the multirate behavior. Furthermore, we construct the relaxation-based circuit simulator DESIRE2 and apply this simulator to the transient analysis of MOS circuits. Finally, we show that the present technique enables to use efficiently the multirate integration method in VSR and reduce the total simulation time without losing the waveform accuracy.