Finite Element Method study on VLF propagable modes coupling and interference in the anisotropic earth-ionosphere waveguide

In this paper, the coupled-mode theory is incorporated into the improved frequency-domain finite element method (FEM) to simulate very low frequency (VLF) propagable modes coupling and interference in the anisotropic Earth-ionosphere waveguide. The matrix equation of the electric field is solved using parallel lower-upper factorization technique to speed up the calculation. The method used to determine the propagation constants for different propagable modes is given. After the FEM is validated by comparing simulated results with the measured data, effects of variable geomagnetic information on the attenuation rate, relative phase velocity, mode coupling, and multiple-mode interference of VLF electromagnetic wave in the anisotropic waveguide are investigated. This work provides an efficient way for improving the prediction accuracy of the VLF communication, positioning, navigation, and timing systems.