A 3D-FDTD+PE hybrid method for predicting the propagation characteristics of low-frequency ground waves in complex terrain of the source area

To address the challenge of predicting the propagation characteristics of low-frequency ground waves in large-scale complex terrains, a hybrid method combining near-field three-dimensional finite-difference time-domain (3D-FDTD) and far-field three-dimensional parabolic equation (3D-PE) is proposed. This approach effectively meets the requirements of electromagnetic calculations for mixed-scale targets in both the local complex source area and the large-scale radiation area. The 3D-FDTD method is adopted in the complex source area to ensure calculation accuracy, while the 3D-PE method is utilized in the relatively flat radiation area to enhance computational efficiency. By performing a time-domain to frequency-domain variable step conversion and secondary windowing processing on the feed source field values, the numerical stability of field value transmission from the source area to the radiation area is guaranteed. After integrating the advantages of two methods, the computational time and memory usage of this method are reduced to 1/12 and 1/15 of the full-area 3D-FDTD method, respectively, under the same accuracy. Furthermore, by combining the source area scenarios with complex terrains such as cliffs and high mountains, a systematic analysis is conducted to determine the influence of the source area's terrain undulations on the propagation characteristics of low-frequency ground waves in the radiation sea area, providing a theoretical basis for the site selection and construction of low-frequency transmitting stations.