Staggered-grid Pseudospectral Time Domain (PSTD) Method Using Real Fourier Transform for 2.5D Electromagnetic Wave Propagation

The staggered grid algorithm was originally invented for achieving better stability and e-ciency in the flnite difierence time domain (FDTD) method for modeling the electromag- netic wave propagation. Seismologists extended the staggered grid approach to the pseudospectral time domain (PSTD) scheme to model seismic wave propagation. However, no detailed formu- lation of the staggered grid approach for electromagnetic (EM) simulations has been explicitly discussed. We present the staggered grid PSTD for EM simulations by shifting the spatial deriva- tives halfway between 2 adjacent nodes and making the Nyquist wave number a non-zero pure real value of i…=¢x. By doing this, the Nyquist information of the original spatial function is preserved, and the difierentiation operator is more stable. In the Fourier domain, adding trigono- metric factors in the classic Fourier coe-cients is equivalent to the staggered grid approach in the original space domain. A staggered grid PSTD algorithm makes the time marching more stable, and numerical dispersion is suppressed for models with sharp contrasts in material properties. In this paper, we have applied the staggered grid PSTD method to 2.5D electromagnetic wave propagation simulations using the real Fourier transform. We discuss this method and apply it to model a Ground Penetrating Radar (GPR) system.