On exponential fitting for circuit simulation

In this paper, the stability and accuracy properties of exponentially-t integration algorithms applied to the test problem x= ?Ax are compared to the more standard backward-Euler and semi-implicit methods. For the analysis, A 2 R nn is assumed to be connectedly diagonally-dominant with positive diagonals, as this models the equations resulting from the way MOS transistors and interconnect parasitics are treated in circuit-level timing simulation programs. Examples are used to demonstrate that all the exponential-tting methods, and the semi-implicit methods, are much less accurate than backward-Euler for tightly-coupled stii problems, and an example is given which destabilizes one of the exponential-tting methods. It is then proved that in the limit of large timesteps, the more stable exponential-tting methods become equivalent to a semi-implicit algorithm. Finally, it is shown that the backward-Euler, semi-implicit, and certain exponentially-t algorithms are multirate A-stable.