Rigorous analysis of numerical phase and group velocity bounds in Yee's FDTD grid

Abstract

We present a systematic derivation of the extreme values of phase and group velocity in Yee's finite difference time domain (FDTD) lattice with unequal aspect ratios. Using a Lagrange multiplier based approach, we derive necessary conditions that propagation vector components need to satisfy to attain extreme values in phase and group velocity. A knowledge of these extreme values are useful in designing low numerical dispersion FDTD schemes and also seeding numerical inversion routines of FDTD dispersion relations. © 2007 IEEE.