The 3D Fractional Modeling of Electromagnetic Sub-Diffusion Based on FDTD

The anomalous diffusion has been discovered in many natural motions, it is defined as a phenomenon that does not conform to FICK's diffusion law. One of the anomalous diffusions is the electromagnetic sub-diffusion, which indicated the power law decay rate is slower than normal -2/5. In this paper, we modeled electromagnetic sub-diffusion based on 3D finite-different time-domain (FDTD) method. Through the introduction of roughness parameter in the definition of conductivity and the discretization of fractional integrations, the electromagnetic sub-diffusion can be efficiently modeled. The improved method is verified by homogeneous half-space models and anomalous models with 3D bodies, the results show that it can model 3D electromagnetic sub-diffusion with high precisions and has a good performance in the recognitions of anomalous bodies.