Efficient Steady-State Analysis Based on Matrix-Free Krylov-Subspace Methods

Gaussian-elimination based shooting-Newton methods, a commonly used approach for computing steady-state solutions, grow in computational complexity like N³, where N is the number of circuit equations. Just using iterative methods to solve the shooting-Newton equations results in an algorithm which is still order N² because of the cost of calculating the dense sensitivity matrix. Below, a matrix-free Krylov-subspace approach is presented, and the method is shown to reduce shooting-Newton computational complexity to that of ordinary transient analysis. Results from several examples are given to demonstrate that the matrix-free approach is more than ten times faster than using iterative methods alone for circuits with as few as 400 equations.