A comparison of numerical dispersion in FDTD and TLM algorithms

Potentially differential methods in the time domain such as finite difference time domain (FDTD) and transmission line matrix (TLM) are attractive for solving electrically large problems, as is often the case when carrying out computations for electromagnetic compatibility. FDTD algorithms that are second order accurate in time and space are inherently dispersive and anisotropic. This can potentially cause computational errors when considering electrically large problems. Using a fine mesh can reduce the numerical dispersion but significantly impacts on the computational resources required. FDTD schemes that are fourth order space and second order time significantly reduces the numerical dispersion with a minimal increase in computational requirements. Symmetrical condensed node TLM has also been used successfully to solve many electromagnetic problems. In this paper, a comparison is made for the dispersion in TLM, 2^nd and 4^th order FDTD when a Gaussian pulse is propagating in a WR90 waveguide. A waveguide was considered to be a good example to consider because the wave propagates at an angle to the axial direction that is frequency dependent. The results show that the TLM and 4^th order FDTD exhibit significantly lower numerical dispersion than 2^nd order FDTD, potentially making them suitable for the accurate solution of large scale EMC problems.