=== EM.Tempo's Mesh Types ===
[[EM.Tempo]] generates a brick volume mesh for FDTD simulation. The FDTD mesh is a rectangular Yee mesh that extends to the entire computational domain. It is primarily constructed from three mesh grid profiles in the XY, YZ and ZX principal planes. These projections together create a 3D mesh space consisting of a large number of cubic volume cells (voxels) carefully assembled in a way that approximates the shape of the original structure.
In [[EM.Tempo]], you can choose one of the three FDTD mesh types:
* Adaptive Mesh
* Fixed-Cell Mesh
[[EM.Tempo]]'s default mesh generator produces an adaptive brick mesh of your physical structure, whose mesh resolution varies with the frequency. As the operating frequency of your project increases, the default '''Adaptive''' FDTD mesh generator creates a larger number of smaller voxels for a given physical structure. The adaptive mesh is optimized in such a way as to capture all the geometric details, curvatures and thin slanted plates or sheets, which often pose a challenge to staircase meshing. It usually provides a reasonably accurate discretization of most complex structures.
Occasionally, you may opt for a more regularized FDTD mesh with almost equal grid line spacings everywhere, but still with a frequency-dependent cell size. In that case, you can use [[EM.Tempo]]'s '''Regular''' FDTD mesh generator, which is indeed a simplified version of its adaptive mesh generator. The regular FDTD mesh enforces only two criteria: minimum mesh density and absolute minimum grid spacing. The grid cell sizes in this mesh are almost uniform in objects of the same material composition or in free-space regions.
[[EM.Tempo]] also offers a uniform, frequency-independent, '''Fixed-Cell''' FDTD mesh generator. The fixed-cell mesh consists of three uniform grids in the XY, YZ and ZX principal planes. However, the uniform mesh cell dimensions along the three direction, i.e. Δx, Δy and Δz do not have to be equal. The fixed-cell mesh generator tries to fit your physical structure to the mesh grid rather than adapting the mesh to your physical structure.
{{Note|When choosing a mesh type for your FDTD simulation, keep in mind that adaptive and regular mesh types are frequency-dependent and their density varies with the highest frequency of your specified bandwidth, while the uniform mesh type is always fixed and independent of your project's frequency settings.}}
=== Discretizing the Physical Structure Using the Adaptive Yee Mesh ===
[[EM.Tempo]]'s default mesh generator creates an adaptive brick volume mesh that uses a variable staircase profile, where the grid line spacings vary with the curvature (derivative) of the object edges or faces. As a result, a higher mesh resolution is produced at "curved" areas to better capture the geometrical details. The resolution of the adaptive FDTD mesh is driven by the '''Mesh Density''', expressed in cells per effective wavelength. Since FDTD is a time-domain method and the excitation waveform may have a wideband spectral content, the effective wavelength is calculated based on the highest frequency of the project: f<sub>max</sub> = f<sub>0</sub> + Δf/2, where f<sub>0</sub> (or fc) is your project's center frequency and Δf (or bw) is its specified bandwidth. In other words, the effective wavelength in the free space is λ<sub>0,eff</sub> = c / f<sub>max</sub>, c being the speed of light in the free space. The effective wavelength in a dielectric material with relative permittivity ε<sub>r</sub> and permeability μ<sub>r</sub> is given by λ<sub>d,eff</sub> = λ<sub>0,eff</sub> / √ε<sub>r</sub>μ<sub>r</sub>.
The adaptive FDTD mesh, by default, produces different grid cell sizes in the free space regions than inside dielectric regions. The effective wavelength in a dielectric material with relative permittivity e<sub>r</sub> and permeability µ<sub>r</sub> is given by λ<sub>d,eff</sub> = λ<sub>0,eff</sub> / √ε<sub>r</sub>μ<sub>r</sub>. Therefore, the average ratio of the cell size in a dielectric region to the cell size in the free space is 1/√(ε<sub>r</sub>μ<sub>r</sub>). The adaptive FDTD mesh generator also takes note of the geometrical features of the objects it discretizes. This is more visible in the case of curved solids, curves surfaces and curved wires or obliquely oriented planes and lines which need to be approximated using a staircase profile. The mesh resolution varies with the slope of the geometrical shapes and tries to capture the curved segments in the best way. Another important feature of the adaptive FDTD mesher is generation of gradual grid transitions between low-density and high-density mesh regions. For example, this often happens around the interface between the free space and high permittivity dielectric objects. Gradual mesh transitions provide better accuracy especially in the case of highly resonant structures.