=== The FDTD Mesh Types ===
[[Image:FDTD80.png|thumb|800px|EM.Tempo's Mesh Settings dialog]][[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 along the XY, YZ and ZX principal planes. These projections together create a 3D rectangular (voxel) mesh spaceconsisting of a large number of cubic 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:
* Fixed-Cell 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 edge or face. 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> is your project's center frequency and Δf (or BW) is its specified bandwidth. Â Â 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.
Occasionally, you may prefer a more regular FDTD mesh with almost equal grid line spacing everywhere, but still with a frequency-dependent cell size. In that case, you can select the "<u>'''Regular'''</u>" option of the '''Mesh Type '''dropdown list in the FDTD Mesh Settings dialog. The regular FDTD mesh enforces only two of the above [[parameters]]: '''Minimum Mesh Density''' and '''Absolute Minimum Grid Spacing'''. Or you may opt for an absolutely "<u>'''Uniform'''</u>" mesh type, for which you need to specify the '''Cell Size '''along the X, Y, Z directions in project units. [[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.
 [[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.
{{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.}}
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Occasionally, you may prefer a more regular FDTD mesh with almost equal grid line spacing everywhere, but still with a frequency-dependent cell size. In that case, you can select the "<u>'''Regular'''</u>" option of the '''Mesh Type '''dropdown list in the FDTD Mesh Settings dialog. The regular FDTD mesh enforces only two of the above [[parameters]]: '''Minimum Mesh Density''' and '''Absolute Minimum Grid Spacing'''. Or you may opt for an absolutely "<u>'''Uniform'''</u>" mesh type, for which you need to specify the '''Cell Size '''along the X, Y, Z directions in project units.
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Mesh_Generation_Schemes_in_EM.Cube#Working_with_Mesh_Generator | Working with Mesh Generator ]]'''.
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[[Image:FDTD80.png|thumb|600px|EM.Tempo's Mesh Settings dialog]]
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EM.Tempo discretizes objects using what is often referred to as the âstaircase approximationâ. In this mesh generation scheme, the structure is recreated using a large number of cubic cells carefully assembled in a way that approximates the shape of the original structure. By default, a carefully calculated, "<u>'''Adaptive'''</u>" mesh of your physical structure is generated in order to satisfy the following criteria:
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Advanced Meshing in EM.Tempo]]'''.