FDTD — finite differences in the time domain

FDTD (finite-difference time-domain) is a fully numerical method that solves Maxwell's equations in the time domain on a global grid covering the Earth-ionosphere cavity. The field is computed step by step in time and the resonance spectrum is obtained by the Fourier transform of the time course.

The main strength of FDTD is that it naturally includes the inhomogeneities of the cavity: the asymmetry between the day and night sides, the smooth conductivity profile of the ionosphere and geographic differences can be entered directly into the grid. The method thus faithfully captures effects that the analytical model of a uniform cavity neglects.

FDTD has been applied not only to terrestrial SR, but also to planetary resonances — three-dimensional FDTD modeling of SR parameters has been carried out for Titan, Venus and Mars Yang 2006. The price for the realism is high computational demand: a fine grid covering the entire planet and many time steps require considerable computational resources.