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 having an irregular structure; parsing characteristic data describing the power delivery network; forming a circuit matrix relating to said characteristic data; regularizing the model; forming from the regularized model a preconditioner matrix with a specialized structure that allows solution with near optimal complexity, the preconditioner matrix having a sparse structure that allows use of a Fast Transform, such sparse structure including off-diagonal blocks which are diagonal matrices and main diagonal blocks which are tridiagonal or block diagonal matrices; 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 to thereby improve performance of the power delivery network based on the circuit and preconditioner solutions, wherein forming the preconditioner matrix includes the steps of: regularizing the power delivery network based on topology information of the nodes of the power delivery network, and forming the preconditioner matrix using a Modified Nodal Analysis method on the regularized power delivery network, and wherein the power delivery network is regularized from an irregular 3D structure into a regular 2D equivalent by: A. determining distinct x- and y-coordinates of all nodes in different layers of the 3D grid, and taking their Cartesian product to specify the location of the nodes in the regular 2D grid; B. disregarding via resistances between layers, collapsing the 3D grid onto the regular 2D grid by adding together all horizontal branch conductances connected in parallel between adjacent nodes in the x-direction of the 2D grid, and all vertical branch conductances connected in parallel between adjacent nodes in the y-direction of the 2D grid, and decomposing conductances of the 3D grid that occupy multiple nodes of the regular 2D grid into a corresponding number of pieces, and adding together node capacitances corresponding to the same regular grid nodes during the collapsing; C. In the regular 2D grid, substituting horizontal branch conductances by their average value in each horizontal rail, and vertical branch conductances by their average value in each vertical slice, with a slice being a part of a rail between two adjacent horizontal rails; D. substituting node capacitances in each horizontal rail by their average value; and E. amortizing total sum of pad conductances of a specific horizontal rail in the regular 2D grid to all nodes of said rail.