The FDTD method is widely applicable to many problems in science and engineering, and is gaining in popularity in recent years due in no small part to the fast increases in computer memory and speed. However, there are many situations when the frequency domain method is useful.
The finite difference frequency domain (FDFD) method utilizes the frequency domain representation of Maxwell's equations. In practice, however, rather than Maxwell's equations, the frequency domain wave equation is more often used, as it is a more compact form, requires only a single field, and does not require interleaving. In this chapter we will focus on the latter method, and give a brief overview of the Maxwell's equations formulation toward the end of the chapter. Because the method uses the frequency domain equations, the results yield only a single-frequency, steady-state solution. This is often the most desirable solution to many problems, as many engineering problems involve quasi–steady state fields; and, if a single-frequency solution is sought, the FDFD is much faster than the transient broadband analysis afforded by FDTD.
FDFD via the wave equation
The simplest way to set up an FDFD simulation is via the wave equation. This method is often most desirable as well; since it does not involve coupled equations, it does not require interleaving or a Yee cell, and all fields (E, H, and J) are co-located on the grid.