Numerical Modeling of Indoor Propagation Using FDTD Method With Spatial Averaging

Abstract

The error in the local mean magnitude of the electric field (E-field), due to the numerical anisotropy, obtained by the finite-difference time-domain (FDTD) method is investigated in this paper. The spatial averaging is applied over a cube. In order to quantify the error, the numerical results are compared with theoretical and measured ones. The comparison between the FDTD method and theory is conducted for two empty rooms with perfect electric conductor walls at 3 and 5 GHz. It is found that averaging over a cube with side length of 3.3 wavelengths ( $\lambda _{0}$ ) ensures a good matching between the local mean magnitude of the FDTD and theoretical E-field—maximum error below 23%, 95th percentile of the error below 6%, and correlation above 0.83. Measurements over a cube at 3 GHz in empty and office environments are performed. The difference between the averaged numerical and measured magnitude of the E-field decreases with increasing the averaging stencil. For empty room, the maximum error in the local mean FDTD results is 46% and for office scenario is 49% if the cube side length is 0.5 $\lambda _{0}$ .