Acoustical finite-difference time-domain simulations of subwavelength geometries

Accurate simulation of wave propagation around subwavelength geometries using standard finite-difference time-domain (FDTD) techniques require a fine spatial and temporal sampling resulting in high computational costs. In this paper an extension to this standard FDTD technique is proposed by means of quasi-stationary solutions on a subwavelength scale. The FDTD equations in the region near the subwavelength geometry are extended with some correction terms of which the magnitude is extracted from the quasi-stationary pressure distribution around these geometries. These pressure distributions can be calculated from the Laplace equation. Using this new technique, FDTD simulations can be based on a more coarse grid, thus reducing computational cost considerably. The accuracy of this technique is mainly determined by the accuracy of the Laplace solutions. This technique was tested with success on the simulation of resonators. It was also shown that the new FDTD equations can be extended to include viscosity effects. (C) 1998 Acoustical Society of America. [S0001-4966(98)06908-2].