Accuracy of TLM solutions of Maxwell's equations

This work investigates the physical origin of the coarseness and dispersion errors influencing TLM solutions of Maxwell's equations, The study is performed by solving the difference equations of the numerical method analytically. The results confirm a reduction of the accuracy of the discrete solution near field singularities, This effect is a consequence of the finite number of spatial modes supported by the discretized domain. The solution of partially filled waveguide is also investigated. The results show that TLM can have positive or negative dispersion, depending on the dielectric filling, excited mode and the geometry. These results are also valid for the finite difference time domain method (FDTD).