The original Yee FDTD algorithm is second-order accurate in both space and time. Numerical dispersion and grid anisotropy errors can be kept small by having a sufficient number of grid spaces per wavelength. Taflove was among the first to rigorously analyze these errors [2]. Taflove was also the first to present the correct stability criteria for the original orthogonal-grid Yee algorithm [3]. With the introduction of more complicated gridding schemes, algorithm stability and accuracy continue to be areas of active research as will be discussed in Sections viii and ix.
The FDTD method can be used to calculate either scattered fields or total fields. When calculating only the scattered fields, the source of the fields is a function of the known incident field and the difference in material parameters from those of the background medium [4,5]. When using total fields, the total fields are often calculated only over an interior subsection of the computational domain [6,7,8] while scattered fields are calculated in the remaining (exterior) portion of the grid. By using scattered fields in this way, the field incident on the absorbing boundary condition (ref. Sec. iii) is more readily absorbed. To obtain this division of the computational domain into scattered-field and total-field regions, the incident field must be specified over the boundary between these two regions. Holland and Williams presented a comparison of scattered-field formulations (i.e., only the scattered fields were computed throughout the computational domain) and total-field formulations (i.e., the total fields were computed in a subdomain that contained the objected under study) [8]. They determined, due to numerical dispersion, the total-field FDTD approach is superior to the scattered-field approach. Furthermore, the scattered-field approach has the disadvantage that it does not easily accommodate nonlinear media. However, for certain problems, such as those that contain only linear media and do not contain shielded cavities, the scattered-field formulation may be the more desired approach [9]. The relative merits of the total-field and scattered-field formulations were also explored by Fang [10].