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.
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机译：我们提出了一种适用于电磁应用的新的非均匀伪谱时域（NUPSTD）方法，其中在将非均匀网格{x / sub i /}转换为统一的{u / sub i /}之前，先将其转换为统一的{u / sub i /}。快速傅里叶变换（FFT）获得空间导数。随后，通过使用插值公式将转换后的空间导数转换回真实空间。所得方案与统一PSTD算法的区别仅在于du / dx的单个因素，并且计算复杂度为O（NlogN）。因此，它保留了统一方案的效率。通过考虑单个电介质板的测试案例，我们演示了该新方法的应用。计算结果与分析解决方案非常吻合，直到离散波长只有3个像元的频率为止。
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