After a brief exposure to different finite difference algorithms and methods, we now focus our attention on the so-called FDTD algorithm, or alternatively the Yee algorithm [1], for time domain solutions of Maxwell's equations. In this algorithm, the continuous derivatives in space and time are approximated by second-order accurate, two-point centered difference forms; a staggered spatial mesh is used for interleaved placement of the electric and magnetic fields; and leapfrog integration in time is used to update the fields. This yields an algorithm very similar to the interleaved leapfrog described in Section 3.5.

The cell locations are defined so that the grid lines pass through the electric field components and coincide with their vector directions, as shown in Figure 4.1. As a practical note, the choice here of the electric field rather than the magnetic field is somewhat arbitrary. However, in practice, boundary conditions imposed on the electric field are more commonly encountered than those for the magnetic field, so that placing the mesh boundaries so that they pass through the electric field vectors is more advantageous. We will have more to say about the locations of field components later in this chapter. Note that the Yee cell depicted in [2, Fig. 3.1] has the cell boundaries to be aligned with the magnetic field components, rather than with the electric field components as in Figure 4.1.