ALGORITHM STUDY OF THE SPACE TRANSFORMATION FACTOR IN THE TRANSFORMED-SPACE NONUNIFORM PSEUDO-SPECTRAL TIME-DOMAIN SCHEME

摘要

In this paper, we explore algorithms for an evaluation of the space transformation factor (STF) in the application of the transformed- space nonuniform pseudo-spectral time-domain (TSNU-PSTD) scheme. We apply these algorithms to both typical propagation problems and scattering analyses. Before implementing the PSTD technique, we first transform nonuniform grids {x{sub}i}, {y{sub}j}, and {z{sub}k} sampled in a real, nonuniform space to uniform ones {u{sub}i}, {v{sub}j}, and {w{sub}k}. Next, we utilize a uniform-sampled, standard FFT and inverse FFT to calculate spatial derivatives in the space domain of (u, v, w). We then convert the spatial derivatives back to the real space (x, y, z) by simply multiplying space transformation factors (STFs) du/dx, dv/dy and dw/dz. For comparison, we adopt both the Lagrange polynomial interpolation and the cubic spline interpolation to carry out the task. In the Lagrange's case, we evaluate those factors by solving for coefficients of the Lagrange polynomials from a Vandermonde linear system; in the cubic spline algorithm, we calculate the factors after solving for values of the second derivative of the interpolating function from a tridiagonal linear system.