Field leakage reduction using a two-dimensional matched numerical dispersion method and high-order cubic curvilinear interpolation [em programmer´s notebook]

In this study, the Total Field/Scattered Field (TF/SF) formulation, one of the methods used for effectively introducing far-field sources into the Finite-Difference Time-Domain (FDTD) Method, is described in detail. The incident fields required for the implementation of the TF/SF formulation were obtained by the Incident Field Array (IFA) Method. The errors introduced in the Incident Field Array Method were presented by numerical examples, and the Matched Numerical Dispersion (MND) Method was applied to a two-dimensional FDTD grid. It was also shown that for wideband pulse excitations, applying the Matched Numerical Dispersion Method to the TF/SF wave source reduced the field leakages nearly 200 dB (subject to double-precision implementation) compared to the Single-Frequency Compensation method for angles of incidence φ = 45. However, a similar improvement could not be obtained for an angle of incidence of φ =30. It was demonstrated that by using higher-order cubic curvilinear interpolation instead of the linear interpolation used in the Incident Field Array Method, the field leakage could be approximately reduced by 70 dB for an angle of incidence of φ = 45 . This higher-order interpolation technique is applicable for any time-dependent plane wave. A 1 GHz sinusoidal wave was used as the incident wave in the simulation.