A new matrix solution technique for general circuit simulation

An intelligent partial Gauss-Seidel scheme (PGS) for general circuit simulation is described. This approach is a novel combination of direct solution using incomplete LU factorization, and iterative solution using Gauss-Seidel relaxation. The method converges faster and more reliably than Gauss-Seidel, while taking a comparable amount of execution time per iteration. Reliable analytic rules are derived such that terms that would be relaxed in Gauss-Seidel are relaxed only if they are considered small by applying these rules. Solution speeds up to ten times faster than direct methods have been demonstrated and higher gains are anticipated for larger circuits. This scheme is robust and accurate for circuits with many different element types, including bipolar transistors, MOSFETs, diodes, inductors, and dependent sources