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Finite difference time domain calculation of three-dimensional phononic band structures using a postprocessing method based on the filter diagonalization

“…One is the accuracy and another is the missing of the eigenfrequencies. Detailed accuracy comparisons between the FDM and the FFT have been made in the related literature [20,21] about the photonic band structure calculation. In this paper, we only give a simple demonstration; see figures 2(a) and (b), which are enlarged partial views of the left and right subfigures of figure 1(b), respectively.…”

“…Therefore the total computation time cannot be reduced significantly if the FDM is directly used as the postprocessing method, even in the 3D case where the FDTD iteration is run with a high computational cost. However, to our knowledge, so far this issue has not been addressed in the literature [19][20][21] on the FDTD method for PTCs.…”

“…In this way, significantly better calculation results are expected to be obtained with relatively few FDTD iterations. The feasibility of this idea has been demonstrated in some related works about the FDTD calculations of the electromagnetic scattering spectra [17,18] and the photonic ( [19][20][21]; http://ab-initio.mit.edu/harminv/) or phononic [13][14][15] band structures, as well as other time-domain simulations [26]. However, the improved postprocessing method should not be too time-consuming; otherwise, fewer FDTD iterations do not necessarily ensure less total computation time.…”

“…In this case, the improved postprocessing method can really reduce the total computation time significantly. The filter diagonalization method (FDM) [19][20][21][22][23][24][25][26], which was originally used to analyze nuclear magnetic resonance signals [22], has been applied in the postprocessing for the FDTD calculation of PTCs [19][20][21]. For the spectral analysis of a time series formed by the superposition of multiple harmonic components (generally termed 'harmonic inversion'), the FDM has significantly higher frequency resolution than not only the FFT, but also some parametric-modeling-based high-resolution spectral estimation (HRSE) methods [27].…”