Conformal equivalent circuit model and leapfrog alternating direction implicit formulation for fast simulation of power delivery network

Abstract

This paper describes a circuit-oriented leapfrog alternating direction implicit (ADI) method applied to a simulation of a power delivery network (PDN). An equivalent circuit model of the PDN is derived by using a recently-proposed conformal modeling technique, in which orthogonal meshes are used along with a treatment to improve the accuracy of the model. Since the conformal equivalent circuit model has a grid-like topology, it is suitable for direction-based algorithms such as an ADI method and the leapfrog ADI method. An advantage of the ADI-based method is that they can use a relatively-large time step size and reduce the total number of time steps in a transient simulation. In addition, the leapfrog ADI method is more efficient than the existing ADI method because its time marching procedure requires less updating processes. As a result, the conformal equivalent circuit model combined with the leapfrog ADI method can be accurate and efficient in modeling and analysis of the PDN.