PGS and PLUCGS-two new matrix solution techniques for general circuit simulation

Two techniques for general circuit simulation, an intelligent, partial Gauss-Seidel scheme (PGS) and a preconditioned conjugate-gradient scheme (PLUCGS), are described. Both techniques are robust and accurate for bipolar and MOS analog and digital circuits. PGS is a novel combination of direct solution, using 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. Solution speeds up to 6 times faster than direct methods have been demonstrated and higher grains are anticipated for larger circuits. The second method, PLUCGS, uses a partial LU factorization as a preconditioner; a vectorized implementation on a CONVEX C-240 computer is 5-7 times faster than the direct solution method with only one-fourth the memory requirements.<>