An extrapolation procedure to shorten time domain simulations

Time-domain simulation algorithms are widely used in the analysis and design of electromagnetic systems. Many of them are characterized by high Qs. Thus, the simulations have to employ many time steps in order to achieve a complete characterization of these systems. This time-consuming computational effort can be avoided if the late instants of time are extrapolated by applying a parametric estimation algorithm. An optimized implementation of a time-domain extrapolation method and a stop criterion are discussed in this paper. The latter criterion is based upon a normalized squared difference between the waveforms extrapolated from two different sets of initial data and it is used as a means to stop the time domain simulation algorithm.