=== The FDTD Mesh Types ===
[[Image:FDTD28.png|thumb|400px|The adaptive FDTD meshes of a metallic sphere.]][[EM.Tempo]]'s FDTD mesh is a rectangular Yee mesh that extends to the entire computational domain. It is primarily constructed from three mesh grid profiles along the XY, YZ and ZX principal planes. These projections together create a 3D rectangular (voxel) mesh space. Straight lines, boxes and rectangular plates whose edges are aligned with the three principal axes are the simplest objects to mesh in EM.Tempo. Such objects preserve their exact shapes after discretization. All the objects with curved edges and curved surfaces or objects with straight edges and flat faces that are not parallel to the principal axes or principal planes (such as oblique lines and slanted lateral faces of a pyramid) are discretized using a staircase (Yee) profile. EM.Tempo's adaptive mesh generator uses a variable staircase profile, where the cell sizes of grid line spacing vary with the curvature (derivative) of the edge or face. As a result, a higher mesh resolution is achieved at "more curvy" areas to better capture the geometrical details. You have the option to choose one of the three FDTD mesh types:
* Adaptive Mesh
* Fixed-Cell Mesh
The default choice is the adaptive mesh, which is a quite sophisticated mesh. 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> 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 adaptive FDTD mesh, however, produces different grid cell sizes in the free space regions and 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.
According to the Courant-Friedrichs-Levy (CFL) stability criterion, the FDTD time step is determined by the smallest cell size in your FDTD mesh. Occasionally, [[FDTD Module]]'s adaptive mesh generator may create extremely tiny grid cells that would result in extremely small time steps. This would then translate into a very long computation time. [[EM.Cube]] offers the "Regular" FDTD mesh generator, which is a simplified version of the adaptive mesh generator. In a regular FDTD mesh, the grid cell sizes stay rather the same in objects of the same material composition. The mesh resolution increases in materials of higher permittivity and/or permeability based on the effective wavelength in exactly the same way as the adaptive mesh. Finally, [[EM.Cube]]'s FDTD Modules offers a "Uniform" FDTD mesh generator. The uniform mesh consists of three uniform grids along the XY, YZ and ZX principal planes. In other words, the grid cell sizes Δx, Δy and Δz are fixed throughout the entire computational domain. In this case, the uniform mesh generator has to fit your physical structure to the fixed mesh, rather than adapting the mesh to your physical structure.
{{isoimg|FDTD35(1).png|The grid cursor on the XY grid plane and its grid coordinates (I, J, K) displayed on the status bar.}}
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===Meshing Arbitrary Geometries===
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Straight lines, boxes and rectangular plates whose edges are aligned with the three principal axes are the simplest objects to mesh in the [[FDTD Module]]. Such objects preserve their shapes exactly after discretization. All the objects with curved edges and curved surfaces or objects with straight edges and flat faces that are not parallel to the principal axes or principal planes need to be discretized using a staircase profile.
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In the cases of oblique lines and slanted faces (like lateral faces of a pyramid), a uniform staircase profile is used by all of [[FDTD Module]]'s three mesh generators. in other words, the cell sizes or grid line spacing remain the same across the edge or face, since the slope is constant. In the case of curved edges and curved faces or surfaces (like a sphere), the uniform and regular mesh generators use a uniform staircase profile. However, the adaptive mesh generator uses a variable staircase profile, where the cell sizes of grid line spacing vary with the curvature (derivative) of the edge or face. As a result, a higher mesh resolution is achieved at "more curvy" areas to better capture the geometrical details.
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{{twoimg|FDTD31(1).png|A pyramidal object with a slanted plate|FDTD32(2).png|An adaptive FDTD mesh}}
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{{twoimg|FDTD26.png||FDTD25.png|}}
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{{twoimg|FDTD27.png||FDTD28.png|}}
The geometry of a sphere and its regular and adaptive FDTD meshes (top and perspective views).
=== FDTD Mesh Settings ===