Simulating transients in semiconductor devices involves numerically solving the time-dependent drift-diffusion equations, usually in two or three space dimensions. Because of the computation cost of these simulations, methods that perform careful domain decomposition so as to exploit parallel processing have received much recent attention. In this paper, we describe using accelerated waveform relaxation (WR) to perform parallel device transient simulation using both clusters of workstations and the IBM SP-2. The accelerated WR algorithms are compared to pointwise direct and iterative methods, and it is shown that the accelerated WR method is competitive on a single processor. In addition, it is shown that with a domain decomposition chosen for rapid iterative method convergence rather than parallel efficiency, the pointwise methods parallelize poorly but the WR method achieves near linear speedup (with respect to the number of processors) on the IBM SP-2.

In this paper we compare accelerated waveform relaxation algorithms to pointwise methods for the transient simulation of semiconductor devices on parallel machines. Experimental results are presented for simulations on small clusters of workstations and on an Intel iPSC/860. The results show that accelerated waveform methods are competitive with standard pointwise methods on serial machines, but are significantly faster on loosely-coupled MIMD machines.

A conjugate-direction based acceleration to the waveform relaxation (WR) algorithm is derived. Experimental results demonstrated the effectiveness of the acceleration when solving the large, sparsely connected algebraic and differential system generated by standard spatial discretization of the 2D time-dependent semiconductor device equations. The waveform conjugate-direction methods were up to 15 times faster than ordinary WR.>

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.>