Pseudospectral method based on prolate spheroidal wave functions for frequency-domain electromagnetic simulations

We apply prolate spheroidal wave functions of order zero as basis functions in the pseudospectral method for frequency-domain electromagnetic simulation problems. Like the traditional pseudospectral frequency-domain (PSFD) methods based on Chebyshev and Legendre polynomial series, the prolate PSFD method yields exponential order of accuracy. In terms of the number of samples utilized per wavelength, the prolate expansion is superior to the Chebyshev and Legendre polynomial series by a factor of π/2. In addition, the prolate PSFD method employs a more uniform spatial grid, achieving better resolution near the center of the domain.