Finite element method study on VLF propagation in the fine Earth-ionosphere waveguide

A fast and highly efficient frequency-domain finite element method (FEM) is developed to simulate propagation characteristics of very low frequency (VLF) waves in the fine Earth-ionosphere waveguide structure containing the transition period between day and night. The FEM is accelerated by embedding the GPU-based parallel LU factorization method. We present an approach for determining the waveguide structure with the VLF transmitter and receiver locations. After validating the method, effects of the time- and location-varying electric density on the amplitude and phase of the VLF wave are investigated. The electric density of the International Reference Ionosphere (IRI) is revised by coupling with the solar zenith angle. Numerical results simulated using the revised IRI model show excellent agreement with the measured data for the VLF wave from Novosibirsk to Qingdao. This work provides a promising way to research VLF electromagnetic properties of the Earth-ionosphere waveguide and improve the prediction accuracy of VLF navigation and communication.