Application of Alternating Direction Implicit (ADI) Algorithm to Staggered-grid PSTD Modeling of Electromagnetic Waves

摘要

By applying the fast Fourier transform (FFT) and inverse transform to represent the spatial derivatives, the pseudo-spectral time-domain (PSTD) method has achieved a spatial grid of only two points per wavelength while maintaining a high accuracy. Its computational speed can be further accelerated by applying alternating-direction implicit (ADI), which makes PSTD works even when the time step exceeds the maximum time step allowed under the Courant-Friedrich-Levy (CFL) condition. However, due to the unsuitability of FFT on non-continuou condition, conventional ADI-PSTD turns to be unstable in media with high property contrast. We have expanded current ADI-PSTD into staggered-grid ADI-PSTD. After applying the staggered-grid approach into our algorithm by shifting the spatial derivatives halfway between 2 adjacent nodes, the stability of the differentiation operators is enhanced. We will discuss the staggered-grid ADI-PSTD method in detail and apply it to the simulation of a half-space model. The analysis and discussion of the results show its advantages and further potential.