Efficient modeling of impulsive ELF antipodal propagation about the Earth sphere using an optimized two-dimensional geodesic FDTD grid

The letter reports the initial application of a geodesic finite-difference time-domain (FDTD) grid to model impulsive extremely low frequency electromagnetic wave propagation about the Earth sphere. The two-dimensional transverse-magnetic grid is comprised entirely of hexagonal cells, except for a small fixed number of pentagonal cells needed for grid completion. Grid-cell areas and locations are optimized to yield a smoothly varying area difference between adjacent cells, thereby maximizing numerical convergence. The new FDTD grid model is considerably superior to our previously reported latitude-longitude grid because it is simpler to construct, avoids geometrical singularities at the poles, executes about 14 times faster, provides much more isotropic wave propagation, and permits an easier interchange of data with state-of-the-art Earth-simulation codes used by the geophysics community. We verify our new model by conducting numerical studies of impulsive antipodal propagation and the Schumann resonance.