Liu Q H
Sch. of Electr. and Comput. Eng., New Mexico State Univ., Las Cruces, NM.
IEEE Trans Ultrason Ferroelectr Freq Control. 1998;45(4):1044-55. doi: 10.1109/58.710587.
A technique based on the combination of Fourier pseudospectral method and the perfectly matched layer (PML) is developed to simulate transient acoustic wave propagation in multidimensional, inhomogeneous, absorptive media. Instead of the finite difference approximation in the conventional finite-difference time-domain (FDTD) method, this technique uses trigonometric functions, through an FFT (fast Fourier transform) algorithm, to represent the spatial derivatives in partial differential equations. Traditionally the Fourier pseudospectral method is used only for spatially periodic problems because the use of FFT implies periodicity. In order to overcome this limitation, the perfectly matched layer is used to attenuate the waves from other periods, thus allowing the method to be applicable to unbounded media. This new algorithm, referred to as the pseudospectral time-domain (PSTD) algorithm, is developed to solve large-scale problems for acoustic waves. It has an infinite order of accuracy in the spatial derivatives, and thus requires much fewer unknowns than the conventional FDTD method. Numerical results confirms the efficacy of the PSTD method.
开发了一种基于傅里叶伪谱方法和完全匹配层（PML）相结合的技术，用于模拟瞬态声波在多维、非均匀、吸收性介质中的传播。该技术不是使用传统时域有限差分（FDTD）方法中的有限差分近似，而是通过快速傅里叶变换（FFT）算法使用三角函数来表示偏微分方程中的空间导数。传统上，傅里叶伪谱方法仅用于空间周期性问题，因为FFT的使用意味着周期性。为了克服这一限制，使用完全匹配层来衰减来自其他周期的波，从而使该方法适用于无界介质。这种新算法称为伪谱时域（PSTD）算法，用于解决大规模声波问题。它在空间导数上具有无限阶精度，因此与传统FDTD方法相比需要的未知数少得多。数值结果证实了PSTD方法的有效性。
