Accelerated waveform relaxation techniques for the parallel transient simulation of semiconductor devices

This thesis contains a description of a novel generalized SOR algorithm for accelerating the convergence of the dynamic iteration method known as waveform relaxation. The new waveform convolution SOR algorithm is presented, along with a theorem for determining the optimal convolution SOR parameter. Both analytic and experimental results are given to demonstrate that the convergence of the waveform convolution SOR algorithm is substantially faster than that of the more obvious ordinary waveform SOR algorithm. To demonstrate the general applicability of this new method, it is used to solve the differential-algebraic system generated by spatial discretization of the time-dependent semiconductor device equations. The accelerated waveform relaxation algorithm is compared to pointwise direct and iterative methods for the transient simulation of semiconductor devices on both serial and parallel machines. In particular, experimental results are presented for simulations on a small cluster of workstations running the Parallel Virtual Machine (PVM) software, as well as for simulations on a 32-processor Intel iPSC/860. The results show that the accelerated waveform method is competitive with standard pointwise methods on serial machines, and is significantly faster on commonly available loosely-coupled MIMD machines. The parallel accelerated waveform method achieves nearly linear speed-up on the 32 processor Intel iPSC/860 hypercube. The strong implication of the results is that, as MIMD machines become more prevalent, accelerated waveform methods may gain in importance for all areas of simulation requiring the solution of initial value problems. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)