A high-order compact-FDTD algorithm for electrically large waveguide analysis

To model electrically large waveguiding structures, the compact-finite-difference time-domain (FDTD) algorithm needs to use severely scaled down time steps to properly contain the rapidly growing numerical dispersion errors with increased operating frequency. In this work, a high-order compact-FDTD algorithm based on fourth-order spatial central finite differencing and fourth-order temporal backward finite differencing is developed. The accuracy and efficiency of this proposed algorithm are verified through its dispersion relation analysis and validated by modeling high-frequency wave propagation through an earth tunnel. The obtained computational efficiency allows this high-order algorithm to model wireless propagation through longitudinally-invariant road and railway tunnels using several hundred compact-FDTD cells as opposed to the several million FDTD cells required by three-dimensional FDTD algorithms.