Implementation of ADI-FDTD subgrids in ground penetrating radar FDTD models

Abstract

Realistic numerical modeling of ground penetrating radar (GPR) using the finite-difference time-domain (FDTD) method could greatly benefit from the implementation of subgrids – supporting finer spatial resolution – into the conventional FDTD mesh. This is particularly important, when parts of the computational domain need to be modeled in detail or when there are features or regions in the overall computational mesh with values of high dielectric constant supporting propagation of waves at very short wavelengths. A scheme that simplifies the process of implementing these subgrids into the traditional FDTD method is presented. This scheme is based on the combination of the standard FDTD method and the unconditionally stable alternating-direction implicit (ADI) FDTD technique. Because ADI-FDTD is unconditionally stable its time-step can be set to any value that facilitates the accurate calculation of the fields. By doing so, the two grids can efficiently communicate information across their boundary without requiring to use a costly time-interpolation scheme. This paper discusses the performance of ADI-FDTD subgrids when implemented into the traditional FDTD method, using different communication schemes for the information exchange at the boundary of the two grids. The developed algorithm, can handle cases where the subgrid crosses dielectrically inhomogeneous media. In addition, results from the comparison between the proposed scheme and a commonly employed purely FDTD subgridding technique are presented.