The nonstandard finite-difference time-domain (NS-FDTD) method, using a rectangular parallelepipeds structured grid, has been proposed to overcome the dispersion and anisotropic errors of the FDTD method. However, the numerical dispersion and the stability condition have not been examined. Furthermore, the method has been defined only in the isotropic grids. This paper investigates the numerical dispersion and the stability condition of the three-dimensional NS-FDTD method for isotropic and nonisotropic grids. The method is compared with the FDTD method. As a result, this method demonstrates highly accurate characteristics and high Courant stability condition.Index Terms-FDTD method, nonstandard FDTD method, numerical dispersion, phase velocity, stability condition.

SUMMARYRecently, the present authors have applied the FDTD (Finite-Difference Time-Domain) method to acoustic problems. FDTD is one of the finite-difference methods in the time domain used in electromagnetic problems. However, in this method, phase errors cannot be neglected in a largescale propagation analysis such as indoor acoustic propagation and they cause problems in the analysis. In order to reduce the phase error, Cole has invented the NS-FDTD (Non-Standard FDTD) method for electromagnetic problems. However, the numerical dispersion and stability condition are not described in Coles paper. Also, the definition is given only for a cubic lattice. In this paper, an application of the three-dimensional NS-FDTD method to acoustic problems is attempted. Further, the method is extended to a rectangular lattice. The numerical dispersion and stability condition of the present method are derived. As a result, it is shown that the present method has much higher accuracy than the FDTD method.

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SUMMARYThe nonstandard FDTD method has been proposed for highly accurate numerical analysis of large structures. However, the conventional nonstandard FDTD has been defined only with isotropic grids, and hence the treatment of arbitrary cavity shapes has been severely restricted. In order to remove this restriction in this paper, the nonstandard FDTD method is extended to more general nonisotropic grids. First, the FD Laplacian for the nonisotropic grids is newly defined. From the expression for decomposition by the first-order difference operator, the nonstandard FDTD equations are derived for nonisotropic grids. The physical meaning of the nonstandard FD method used in the nonstandard FDTD method is clarified. Next, by means of the nonstandard FDTD method extended to nonisotropic grids, a scattering analysis of large-scale cavities is performed and its effectiveness is demonstrated. The results obtained by the nonstandard FDTD method agree well with the measured values, confirming that the nonstandard FDTD method is effective as a highly accurate scattering analysis method for large-scale cavities. © 2001 Scripta Technica, Electron Comm Jpn Pt 2, 84(12): 816, 2001