Pseudospectral Time-Domain (PSTD)
The Pseudospectral Time-Domain (PSTD) method was first proposed in the 1970s to numerically solve partial differential equations. The basic idea of the PSTD method is to use a set of basis functions to represent the original solution and use the solution sampled at the collocation points to determine the projection of the solution onto the basis functions and obtain the spatial derivatives analytically in the spectral domain. Ideally, the PSTD method is able to achieve spectral accuracy with the computation complexity similar to a high-order finite difference method.

There are two broad categories of Pseudospectral methods in computational electromagnetics depending on the basis function used. One is the Fourier PSTD, which assumes a periodic boundary condition and use Fourier series as basis functions. The other is the so-called multi-domain PSTD, which use Chebyshev or Legendre polynomials defined in a closed domain as basis functions. Compared with other time-domain techniques, PSTD offers tremendous savings in memory, with a much smaller sampling rate. This is very advantageous for electrically large problems.