Transformed-space non-uniform pseudo-spectral time domain (NU-PSTD) algorithm without the use of the non-uniform FFT

We present a new non-uniform pseudo-spectral time domain (NUPSTD) method for electromagnetic applications, in which we transform a non-uniform grid {x/sub i/} into a uniform one {u/sub i/} before applying the fast Fourier transform (FFT) to obtain the spatial derivatives. The transformed spatial derivatives are subsequently converted back to the real space via the use of interpolation formulas. The resultant scheme differs from the uniform PSTD algorithm only by a single factor of du/dx, and has a computational complexity of O(NlogN); hence, it preserves the efficiency of the uniform scheme. We demonstrate the application of the new method by considering the test case of a single dielectric slab. The computed results are in excellent agreement with the analytical solution up to frequencies for which the discretization size is only 3 cells per wavelength.