Waveform relaxation algorithm based on virtual state formulation and its numerical stability

A description is presented of the waveform relaxation (WR) algorithm with the virtual state formulation technique, where adaptive virtual capacitors are interposed for numerical stability. First, the authors present the virtual state relaxation (VSR) method for the stable convergent simulation of nonlinear circuits. The VSR method is applied to the WR algorithm to exploit the multirate behavior. It is shown that the method allows the use of large timestep sizes in numerical integration, and reduces the total simulation time considerably