Investigation into the Selection Methodology of Influencing Factors and Application within the WLP-FDTD Framework

Commencing with the fundamental equations of the WLP-FDTD method, this paper elucidates and analyzes the necessity of the time scale s and the Laguerre order q, along with their impact on the WLP-FDTD method. By leveraging the differential equation of the Laguerre polynomial as a starting point and employing its orthogonality through mathematical transformations, we derive the relationship between s and q. In the verification phase, s is initially selected based on minimizing error while considering bandwidth and excitation signal. Subsequently, the selection of q in the WLP-FDTD method is validated under both rectangular and cylindrical coordinate systems. Overall, in the study of the WLP-FDTD method, determining the time scale and Laguerre order can effectively identify issues affecting computational efficiency and accuracy, thereby avoiding unnecessary trials and reducing research costs.