Click here to learn more about [[Differential Form of Maxwell's Equations]].
Since FDTD is a finite domain numerical technique, the computational domain of the problem must be truncated. At the boundaries of the computational domain, proper boundary conditions must be enforced. In a shielded structure, all objects are enclosed within a perfect electric (or magnetic) conductor box. In an open boundary problem like an antenna, some kind of absorbing boundary conditions such as a perfectly matched layer (PML) must be used to emulate the free space. The computational domain is must be discretized using an appropriate meshing scheme. EM.Tempo uses a non-uniform, variable, staircase (pixelated) Yee mesh with a mesh density that you can customize. A fixed-cell mesh generator is also available, where you can set constant cell dimensions along the three principal axes for the entire computational domain. The variable mesh density is specified in terms of the effective wavelength inside material media. As a result, the mesh resolution and average mesh cell size differ in regions that are filled with different types of material. [[EM.Cube]]'s non-uniform mesher generates more cells in the areas that are occupied by dielectric materials, fewer cells in the free space regions and no cells inside (impenetrable) PEC regions. [[FDTD Module]]'s default "adaptive" mesh generator also refines the mesh around curved segments of lines, surface or solids to produce a far more accurate representation of your geometry. The example below illustrates a dielectric ellipsoid and a 3D view of its Yee mesh:
{{Twoimg|FDTD93.png|A Dielectric Object...|FDTD94.png|...and its Yee mesh.}}
===Differential Form of Maxwell's Equations===Â ===Waveform, Bandwidth & Stability===The FDTD method provides a wideband simulation of your physical structure. In order to produce sufficient spectral information, an appropriate wideband temporal waveform is needed to excite the physical structure. Â The choice of the waveform, its bandwidth and time delay are important for the convergence behavior of the FDTD time marching loop. By default, [[EM.Cube]] Tempo uses a modulated Gaussian waveform with optimal [[parameters]]: t = 0.966/Δf and t<sub>0</sub> = 4.5t, where Δf is the specified bandwidth of the simulation. The time delay t<sub>0</sub> is chosen so that the temporal waveform has an almost zero value at t = 0.
Another issue of concern in an FDTD simulation is the numerical stability of the time marching scheme. You can set the mesh grid cell size to any fraction of a wavelength. Normally, you would expect to get better and more accurate results if you increase the mesh resolution. However, the time step is inversely proportional to the maximum grid cell size in order to satisfy the Courant-Friedrichs-Levy (CFL) stability condition. A high resolution mesh requires a smaller time step. Since you need to let the fields in the computational domain fully evolve over time, a smaller time step will require a larger number of time steps to achieve convergence. [[EM.Cube]] automatically chooses a time step that satisfies the CFL condition.