The nonstandard FDTD method for three-dimensional acoustic analysis and its numerical dispersion and stability condition

Recently, 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 large-scale 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 Cole's 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. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(9): 15–24, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1115