Parallel Algorithms for a Direct Circuit Simulator 1 Techniques for Parallel Circuit Analysis

The DC analysis and transient analysis parts of the general electrical circuit analysis program ESACAP are parallelized to run on the Intel iPSC. Most of the program runs unchanged on the cube manager. Only the solution of the systems of nonlinear algebraic equations is parallelized to run on the hypercube parallel computer. The nonlinear equations arise either from the DC problem or from the discretization of the diierential equations by backward diierentiation formulas. The time domain analysis of analogue circuits or digital circuits at the circuit level involves the numerical solution of systems of nonlinear ordinary diierential equations. The diierential equations are usually stii which implies that implicit numerical integration formulas must be used. Besides, models of electrical circuits often lead to coupled systems of diierential and algebraic equations, and consequently each time step involves the solution of a system of nonlinear algebraic equations including the discretization of the diierential equations. Let a circuit be described by the following implicitly given system of diierential algebraic equations, f (t; y; y 0) = 0 (1) (2) where h is the stepsize in time, h = t n ? t n?1 and y n y(t n).