A Stable Subgridding 2D-FDTD Method for Ground Penetrating Radar Modeling

The subgridding finite-difference time-domain (FDTD) method has a great attraction in ground penetrating radar (GPR) modeling. The challenge is that the interpolation of the field unknowns at the multiscale grid interfaces will aggravate the asymmetry of the numerical system which results in its instability. In this paper, an explicit unconditionally stable technique for a lossy object is introduced into the subgridding FDTD method. It removes the eigenmodes of the coefficient matrix which make the algorithm unstable. Therefore, the proposed approach not only maintains the advantages of simple implementation of the traditional FDTD method but also adopts a relatively large time step in both coarse and fine grid, which breaks through the restriction of the Courant-Friedrichs-Lewy (CFL) stability condition. The proposed method is applied in simulating the transverse magnetic (TM) wave backscattering of the two-dimensional buried objects in lossy media. Its accuracy and efficiency are examined by comparison with conventional FDTD and subgridding FDTD approaches.