Hybrid Sub-Gridded Time-Domain Method for Ground Penetrating Radar Simulations Including Dispersive Materials

Abstract

Based on the explicit finite-difference time-domain (FDTD) and implicit Crank–Nicolson (CN) FDTD methods, this paper presents a hybrid sub-gridded scheme whose time step size depends on the coarse grid size for numerically simulating the 3-D ground penetrating radar (GPR) scenarios in lossy, dispersive, and inhomogeneous soils. The time step size of CN-FDTD is independent of the grid size in the dense grid region due to its unconditional stability. Thus, the whole region can be run with a time step size determined by the coarse grid in an absolutely stable fashion. Moreover, a multi-pole Debye dispersion model, solved with auxiliary differential equations (ADEs) for both FDTD and CN-FDTD, is incorporated to simulate realistic GPR scenarios, including the detection of different objects buried in dispersive soils. In order to reduce the matrix size of the 3-D implicit CN-FDTD method, the domain decomposition technique is originally employed to achieve fast calculation. Several numerical examples of the GPR scenarios are provided to demonstrate the accuracy and efficiency of the hybrid sub-gridded ADE-FDTD method.