On the Numerical Stability of the Precise Integration Time-Domain (PITD) Method

In this letter, the stability issue of the recently proposed 3-D precise integration time-domain (PITD) method is reinvestigated. It is found that the PITD is not unconditionally stable; its stability condition is strongly dependent on the preselected number of sub time-steps and sizes of numerical cells as well as the order of the approximation used. However, since the upper limit of time step is found to be proportional to the number of sub time-steps, the time step can be of a value much larger than the Courant–Friedrich–Levy limit of the conventional finite difference time domain. Numerical examples are presented to verify our analysis.