Abstract: In one embodiment, a method comprising identifying a sub-network of the linear circuit, the sub-network having one or more internal nodes, one or more interface nodes, and branches connecting the one or more internal nodes and the one or more interface nodes, the sub-network having at least one of a capacitor and an inductor, is described. The method in one embodiment comprises determining a linear equation system for transient simulation of the linear circuit, the linear equation system containing no variable representing the one or more internal nodes.

Abstract: Methods and apparatuses for transient simulation of circuits. One embodiment of the present invention eliminates the inductive branch current variables in terms of node voltage variables to generate a linear equation system with a sparse, symmetric and positive definite matrix, which can be solved efficiently using a pre-conditioned conjugate gradient method. The known vector of the linear equation system includes the contribution from the known inductive branch currents at a previous time instance. In one embodiment of the present invention, a node on a branch to a known voltage, such as ground, and on two resistive branches are identified and eliminated to form the linear equation system with a reduced dimension. In one embodiment of the present invention, multiple time step sizes are selectively used to balance the accuracy in transient simulation and efficiency.