On Exponential Fitting For Circuit

In this paper we present our results on the stability and accuracy properties of exponentially-t integration algorithms, and demonstrate these properties on some test examples. We consider the multivariate test problem x= ?Ax where A 2 < nn and is assumed to be irreducibly diagonally-dominant with positive diagonals, as this models the equations resulting from the way MOS circuits are treated in timing simulation programs. It is shown that for these problems, the CINNAMON exponentially-t algorithm is A-stable, and an example is given where the algorithm in XPSim is unstable. A semi-implicit version of the XPSim algorithm is then described, and it is shown that this semi-implicit algorithm is A-stable. Examination of examples demonstrate that neither the stabilized XPSim algorithm nor the CINNAMON algorithm produces satisfactory results for very large timesteps. The eeect of ordering on the accuracy and stability of the integration methods is also examined , and it is shown that ordering always enhances accuracy, though not signiicantly for large timesteps, and that the XP-Sim algorithm can be made more stable with a carefully chosen ordering.