Parallel Algorithms for a Direct Circuit Simulator

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 differential equations by backward differentiation formulas. 1 Techniques for Parallel Circuit Analysis The time domain analysis of analogue circuits or digital circuits at the circuit level involves the numerical solution of systems of nonlinear ordinary differential equations. The differential equations are usually stiff which implies that implicit numerical integration formulas must be used. Besides, models of electrical circuits often lead to coupled systems of differential and algebraic equations, and consequently each time step involves the solution of a system of nonlinear algebraic equations including the discretization of the differential equations. Let a circuit be described by the following implicitly given system of differential algebraic equations, f(t, y, y′) = 0 (1) where f : R×R ×R → R . When discretized by the simple backward Euler formula, the following nonlinear algebraic system is obtained, f(tn, yn, (yn − yn−1)/h) = 0 (2) where h is the stepsize in time, h = tn − tn−1 and yn ≈ y(tn). The solution of (2) is obtained by some iterative method, usually of Newton type, y n = y (m) n − F ′ n(y (m) n ) fn(y (m) n ) (3) where fn(y) = f(tn, y, (y − yn−1)/h) and F ′ n(y) = ∂fn(y)/∂y. ∗Published in Proceedings of the 10’th European Conference on Circuit Theory and Design, September 1991, Copenhagen, Denmark, Erik Lindberg (Edt.), pp. 314 – 323.