Changes

EM.Tempo

856 bytes removed, 20:56, 31 July 2015
/* Generating the FDTD Mesh */
[[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 ]]'''.
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> + &Delta;f/2, where f<sub>0</sub> is your project's center frequency and &Delta;f (or BW) is its specified bandwidth. In other words, the effective wavelength in the free space is &lambda;<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 e<sub>r</sub> and permeability µ<sub>r</sub> is given by &lambda;<sub>d,eff</sub> = &lambda;<sub>0,eff</sub> / &radic;&epsilon;<sub>r</sub>&mu;<sub>r</sub>.
The adaptive FDTD mesh, however, produces different grid cell sizes in the free space regions and inside dielectric regions[[Image:Info_icon. The effective wavelength in a dielectric material with relative permittivity e<sub>r</sub> and permeability µ<sub>r</sub> is given by &lambda;<sub>d,eff</sub> = &lambda;<sub>0,eff</sub> / &radic;&epsilon;<sub>r</sub>&mu;<sub>r</sub>. Therefore, the average ratio of the cell size in a dielectric region png|40px]] Click here to the cell size in the free space is 1/&radic;(&epsilon;<sub>r</sub>&mu;<sub>r</sub>). The adaptive FDTD mesh generator also takes note of the geometrical features of the objects it discretizes. This is learn 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 profileabout '''[[Mesh_Generation_Schemes_in_EM. The mesh resolution varies with the slope of the geometrical shapes and tries to capture the curved segments in the best wayCube#EM. Another important feature of the adaptive FDTD mesher is generation of gradual grid transitions between low-density and high-density mesh regionsTempo. For example, this often happens around the interface between the free space and high permittivity dielectric objects27s_Adaptive_Brick_Mesh_Generator | EM. Gradual mesh transitions provide better accuracy especially in the case of highly resonant structuresTempo's Adaptive Brick Mesh Generator]]'''.
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.
{{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.}}
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Mesh_Generation_Schemes_in_EM.Cube#Working_with_Mesh_Generator The_Fixed-Cell_Brick_Mesh_Generator | Working with The Fixed-Cell Brick Mesh Generator ]]'''.
<table>
28,333
edits