A new numerical method for large-scale complex media: the PSTD algorithm

Conventional finite-difference time-domain (FDTD) methods are very inefficient for simulations of electromagnetic wave propagation in large-scale complex media. This is mainly because of the low-accuracy associated with the spatial discretization in the FDTD methods. As a result, even for a moderate size problem, a large number of cells (typically 10-20 cells per wavelength) are required to obtain reasonably accurate results. This requirement becomes much more stringent for large-scale problems since the dispersion error grows rapidly with the propagation distance. The authors recently developed a pseudospectral time-domain (PSTD) method which requires only two cells per wavelength regardless of the problem size. In terms of the spatial discretization, this method is an optimal time-domain solution since it has an infinite order of accuracy in the spatial representation. For a problem of size 32 to 512 wavelengths in each dimension, the PSTD method is at least 4 ^D-32^D times more efficient than the FDTD method (where D is the dimensionality of the problem). For larger problems, the advantage of the PSTD method becomes even more profound. Therefore, the PSTD method is ideal for simulations of electromagnetic wave propagation in large-scale complex media