研究目的
To propose a novel FDTD scheme for the analysis of general frequency-dependent media including the Cole–Cole, Davidson–Cole, and Havriliak–Negami relaxations, circumventing the discretization of the fractional derivatives in the time-domain representation by using the fast inverse Laplace transform (FILT) and Prony’s method.
研究成果
The proposed FDTD scheme is robust and can model any kind of complex permittivity function in which the inverse Laplace transform can be found numerically. Numerical simulations demonstrate good agreement with analytical results, validating the method.
研究不足
The proposed method requires more memory and computational costs compared to conventional methods such as the ADE approach and is heavily dependent on multiple approximation methods of the FILT and Prony’s method, which may cause numerical instability.
1：Experimental Design and Method Selection:
The proposed FDTD scheme combines the FILT and Prony’s method to derive the relative permittivity in the z-domain, which is then incorporated into the FDTD method.
2：Sample Selection and Data Sources:
The method is applied to dispersive media with complex permittivity represented by Debye, Cole–Cole, Davidson–Cole, and Havriliak–Negami functions.
3：List of Experimental Equipment and Materials:
The FDTD method is utilized with specific parameters for each medium type.
4：Experimental Procedures and Operational Workflow:
The FILT is first used to convert the dispersion expression into an impulse response in the time domain, followed by Prony’s method to extract model parameters and represent the time-domain responses in the z-domain.
5：Data Analysis Methods:
The reflection coefficients are calculated and compared with analytical results to validate the proposed FDTD scheme.
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