Efficient Finite-difference Time-domain GPR Modeling Using Subgrids

The well-known finite-difference time-domain (FDTD) approach to the numerical solution of Maxwell’s equations for ground penetrating radar (GPR) modeling has a conditionally stable nature and this is one of the major limitations of the FDTD scheme. For the stability condition to be fulfilled, the maximum allowable time-step for the numerical computations is limited by the minimum cell size in the computational domain. Therefore, when detailed structures need to be simulated and/or when there are small features or regions of limited extent in the overall computational mesh with values of high dielectric constant - supporting propagation of waves at very short wavelengths - the spatial-step should be small enough so as all the objects in the computational domain are adequately resolved. For such cases, the FDTD solution employing a small, uniform spatial-step in the whole computational domain would lead to substantial computer memory requirements and execution time increase. This problem can be overcome and efficiency can be increased by introducing subgrids, into the FDTD method. Examples of areas of applications of these subgrids include the efficient modelling of fractures and other small targets as well as targets with high values of dielectric constant.