Finite-difference and pseudospectral time-domain methods for subsurface radar applications

The finite-difference time-domain (FDTD) method is widely applied to simulate transient electromagnetic wave propagation. In this method, the spatial and temporal derivatives in Maxwell´s equations are approximated by finite differences. Numerical experiments show that accurate results require a fine discretization of about 8-20 grids per wavelength at the highest frequency being simulated. To increase the efficiency of time-domain solutions, various spectral-domain techniques have been developed to reduce the grid density. In particular, the pseudospectral time-domain (PSTD) method uses a fast Fourier transform (FFT) algorithm to represent the spatial derivatives in Maxwell´s equations, and provides accurate results with only two grids per wavelength. This article compares the FDTD and PSTD methods in terms of their development and capabilities in the simulations of subsurface radar applications. Numerical examples are used to demonstrate their relative accuracy and efficiency for different problems.