Recent advances in sparse linear solver technology for semiconductor device simulation matrices

Abstract

This paper discusses recent advances in the development of robust direct and iterative sparse linear solvers for general unsymmetric linear systems of equations. The primary focus is on robust methods for semiconductor device simulations matrices, but all methods presented are solely based on the structure of the matrices and can be applied to other application areas e.g. circuit simulation. Reliability, a low memory-footprint, and a short solution time are important demands for the linear solver. Currently, no black-box solver exists that can satisfy all criteria. The linear systems from semiconductor device simulations can be highly ill-conditioned and therefore quite challenging for direct and preconditioned iterative solver. In this paper, it is shown that nonsymmetric permutations and scalings aimed at placing large entries on the diagonal greatly enhance the reliability of direct and iterative methods. The numerical experiments indicate that the overall solution strategy is both reliable and very cost effective. The paper also compares the performance of some common software packages for solving general sparse systems.