Finite element method simulation on propagation characteristics of very low frequency and low frequency waves

For land-based radio navigation and timing systems, the propagation of very low frequency (VLF)/low frequency (LF) waves is simulated based on the frequency-domain finite element method, to address the challenge of rapidly predicting electromagnetic properties of radio waves in the complicated Earth-ionosphere waveguide. By introducing the transfer function method, the spatial broadband complex transfer function extracted by the finite element method is mapped to the time domain. Transient waveform reconstruction and the extraction of additional secondary delay are accomplished. The accuracy of the finite element method is validated by comparison with results in the reference. Effects of topographic undulations, ionospheric parameters, propagation distance, and working frequency on the amplitude and phase of radio waves are numerically computed. This work provides powerful technical support for the evaluation, system design and optimization deployment of radio navigation and timing technologies, as well as rapid and accurate prediction of the amplitude and phase of signals.