1. A method for simulating the time-varying responses of a plurality of points of a power delivery network of approximately N nodes, comprising: selecting a model of a power delivery network of a circuit; parsing characteristic data describing the power delivery network; forming a circuit matrix relating to said characteristic data; forming a preconditioner matrix with a specialized structure that allows solution with near optimal complexity such as O(N log N); solving said circuit and preconditioner matrices with an iterative linear equation solution algorithm, using one or more processors; and reporting the responses at selected nodes and branches of the power delivery network.