Waveform relaxation for transient simulation of two-dimensional MOS devices

Abstract

The authors present experimental results demonstrating the effectiveness of waveform relaxation (WR) for solving the large, sparsely connected algebraic and differential system generated by standard spatial discretization of the two-dimensional time-dependent semiconductor device equation. The experiments demonstrate that WR converges in a uniform manner, and that there is typically some multirate behavior in a device that the WR algorithm can exploit. Speed and accuracy comparisons are made between standard direct methods, red/black Gauss-Seidel WR, and red/black overrelaxed WR. For their experiments, calculated terminal currents matched well between the methods, and overrelaxed WR was up to a factor of 3 faster than direct methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>