The Effects of Unsymmetric Matrix Permutations and Scalings in Semiconductor Device and Circuit Simulation

Abstract

The solution of large sparse unsymmetric linear systems is a critical and challenging component of semiconductor device and circuit simulations. The time for a simulation is often dominated by this part. The sparse solver is expected to balance different, and often conflicting requirements. Reliability, a low memory-footprint, and a short solution time are a few of these demands. Currently, no black-box solver exists that can satisfy all criteria. The linear systems from both simulations can be highly ill-conditioned and are, therefore, quite challenging for direct and iterative methods. In this paper, it is shown that algorithms to place large entries on the diagonal using unsymmetric permutations and scalings greatly enhance the reliability of both direct and preconditioned iterative solvers for unsymmetric linear systems arising in semiconductor device and circuit simulations. The numerical experiments indicate that the overall solution strategy is both reliable and cost effective.