An Efficient 2-D Compact Precise-Integration Time-Domain Method for Longitudinally Invariant Waveguiding Structures

Based on both the compact technique and the precise-integration (PI) technique, a 2-D compact precise-integration time-domain method (CPITD) is developed in order to mitigate the rapidly growing numerical dispersion errors of a recently proposed compact finite-difference time-domain (FDTD) algorithm with increased time-step size when modeling electrically large and longitudinally invariant waveguiding structures. The stability condition and the dispersion equation of the new algorithm are both derived analytically. The provided enhancement over the FDTD, compact FDTD, and the conventional PITD methods is exhibited through theoretical examination of the dispersion performance, and subsequently, validated by means of numerical experimentation. It is found that with the PI technique, the maximum limit of the time step allowable by the new algorithm's stability criterion is much larger than the Courant-Friedrich-Levy limit of the compact-FDTD method, more particularly, numerical dispersion errors can be made nearly independent of time-step size, i.e., an appreciable reduction of numerical dispersion error is achievable at any time-step size in the simulations. Numerical experimentations of typical waveguide structures verify and validate the very promising theoretical results. This CPITD algorithm will be very useful in electrically large and longitudinally invariant waveguiding structures since the decreased number of grid points in the 2-D domain greatly reduces the memory requirements and also the overall computational time, and the PI technique nearly removes the impact of time-step size on the numerical dispersion, and as a consequence, significantly reduces numerical dispersion error for any time-step size.