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Transformed‐space nonuniform pseudospectral time‐domain algorithm
Author(s) -
Leung WingKai,
Chen Yinchao
Publication year - 2001
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/1098-2760(20010320)28:6<391::aid-mop1051>3.0.co;2-5
Subject(s) - fast fourier transform , interpolation (computer graphics) , fourier transform , pseudo spectral method , discrete fourier transform (general) , algorithm , mathematics , grid , mathematical analysis , reflection (computer programming) , microwave , space (punctuation) , domain (mathematical analysis) , geometry , physics , computer science , fourier analysis , fractional fourier transform , telecommunications , classical mechanics , operating system , motion (physics) , programming language
In this paper, a new nonuniform pseudospectral time‐domain (NU–PSTD) method is presented for electromagnetic applications. In this method, we transform a nonuniform grid { x i } into a uniform one { u i } before applying the fast Fourier transform (FFT) to obtain the spatial derivatives. These transformed‐space derivatives are then converted back to the real space via interpolation formulas. The resultant scheme differs from the uniform PSTD algorithm by a single factor of du / dx only, and is therefore equally efficient with a computational complexity of O ( N log N ). We demonstrate the new method with calculations of the reflection coefficients of a single and a coated dielectric slab. In both cases, the computed results are in excellent agreement with the analytic solution for frequencies up to only three cells per wavelength. We also discuss an alternative formulation of the NU–PSTD method based on the nonuniform discrete Fourier transform (NU–DFT). We find that this formulation is unstable, except for grids that are very nearly uniformly. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 28: 391–396, 2001.