Waveform relaxation algorithm with virtual state formulation technique and its multirate behavior

Describes the waveform relaxation (WR) algorithm with the virtual state formulation technique and the effect of multirate behavior in this algorithm. First, the authors present the virtual state relaxation (VSR) method for the simulation of nonlinear circuits, where the virtual state formulation (VSF) technique based on insertion of the adaptive virtual capacitors is utilized for numerical stability. Next, they introduce the VSF technique into WR algorithm in order to exploit the multirate behavior effectively. Finally, they apply the algorithm to MOS circuit analysis, and show that the method enables one to use the large timestep sizes in numerical integration and reduce the total simulation time considerably without losing waveform accuracy