Spherical ADI FDTD Method With Application to Propagation in the Earth Ionosphere Cavity

The alternating direction implicit (ADI) finite-difference time-domain (FDTD) technique is implemented using the spherical coordinate system and applied to wave propagation in the lossy Earth ionosphere cavity. The paper shows, for the first time, that the ADI technique can be developed in conjunction with spherical FDTD in order to overcome the typically long computing times involved in Earth ionosphere cavity problems. Numerical accuracy of the full wave three-dimensional (3D) ADI implementation is validated by comparison with spherical FDTD results. While not free from late time instability, transient responses are shown to be obtained accurately for time steps as large as 15 times the time step derived from cells at the Equator. Hence the spherical ADI is demonstrated to be a promising technique to efficiently characterize Schumann resonances and other complex propagation phenomena around the Earth, while overcoming the space cell eccentricity typically generated by spherical grids.