A Band Relaxation Algorithm for Reliable and Parallelizable Circuit Simulation

A variableband relaxation algorithm for solving large linear systems is developed as an alternative to Gaues-Jacobi relaxation. This algorithm seeks to improve the reliability of Gauss-Jacobi relaxation by extracting a variable-sized band from the matrix and solving that band directly. This leads to a relaxation algorithm with provably better convergence prop erties. Furthermore, this algorithm can be used effectively on a massively parallel computer, because band matrices can be solved in log(n) time on f processors. Test results are presented which compare the convergence properties of variableband relaxation to Gauss-Jacobi relaxation.