Using the classical waveform relaxation method for solving large systems of ordinary differ- ential equations in parallel leads to a slow and non-uniform convergence over the time interval for which the equations are integrated. To improve performance, a new class of waveform relaxation methods known as optimized waveform relaxation algorithms were developed which greatly improve the convergence by using new transmission conditions. These conditions are responsible for the exchange of information between the subsystems which we obtain by decomposing the original large system of differential equations. The waveform relaxation methods were first introduced for solving VLSI circuit simulations, and have been extended to time dependent PDE’s. This talk consists of two parts as follows.

Part-I: in this talk we mainly introduce the classical, optimal and optimized WR algorithms for VLSI circuits, and show the real-world circuit simulations.