Changes

# Click the OK button of the dialog to return to the project workspace.
You can change the mesh algorithm from the dropdown list labeled '''Mesh Type''' if there is more than one option. You can also enter a different value for '''Mesh Density''' in cells per effective wavelength (&lambda;<sub>eff</sub>). For each value of mesh density, the dialog also shows the average &quot;Cell Edge Length&quot; in the free space.
 
== Adding Fixed Grid Points to the Adaptive Yee Mesh ==
 
Adding fixed grid points to an FDTD mesh increases its resolution locally. Each fixed grid point adds three grid lines along the three principal axes passing through that point. You can add as many fixed grid points as you desire and create dense meshes at certain regions. Fixed grid points appear as grey points in the project workspace. To insert a new fixed grid point, follow these steps:
 
* Open the Fixed Grid Points Dialog by selecting '''Menu > Simulate > Discretization > Fixed Grid Points...''' or by right-clicking on the '''FDTD''' '''Mesh''' item of the navigation tree and selecting '''Fixed Grid Points Settings...'''
* Click the {{key|Add/Edit}} button to open the "Add Fixed Grid Point" dialog.
* Enter the (X, Y, Z) coordinates of the new fixed point in the coordinate boxes and click the {{key|OK}} button.
* To modify the coordinates of an existing fixed grid point, select it from the table and click the {{key|Add/Edit}} button.
* You can also remove a fix grid point from the FDTD mesh using the {{key|Delete}} button.
 
<table>
<tr>
<td> [[Image:FDTD36.png|thumb|left|480px|A user-defined fixed grid point in an FDTD mesh.]] </td>
</tr>
<tr>
<td> [[Image:FDTD38.png|thumb|left|480px|Adding a new fixed grid point in EM.Tempo's fixed grid points settings dialog.]] </td>
</tr>
<tr>
<td> [[Image:FDTD39.png|thumb|left|480px|The "Add Fixed Grid Point" dialog.]] </td>
</tr>
</table>
 
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.
 
== Profiling the Brick Mesh ==
 
A volumetric brick mesh is overwhelming for visualization in the 3D space. For this reason, [[EM.Cube]]'s mesh view shows only the outline of the cells on exterior surface of the (staircased) meshed objects. The mesh grid planes provide a 2D profile of the mesh cells along the principal coordinate planes. To display a mesh grid plane, select '''Menu > Simulate > Discretization > Grid Planes >''' and pick one of the three options: '''XY Plane''', '''YZ Plane''' or '''ZX Plane'''. You may also right click on one of the '''XY Plane''', '''YZ Plane''' or '''ZX Plane''' items in the '''Discretization''' section of the navigation tree and select '''Show''' from the contextual menu.
 
While a mesh grid plane is visible, you can move it back and forth between the two boundary planes at the two opposite sides of the computational domain. You can do this in one of the following four ways:
 
* Using the keyboard's Page Up {{key|PgUp}} key and Page Down {{key|PgDn}} key.
* By selecting '''Menu > Simulate > Discretization > Grid Planes > Increment Grid''' or ''' Decrement Grid'''.
* By right clicking on one of the '''XY Plane''', '''YZ Plane''' or '''ZX Plane''' items in the '''Discretization''' section of the navigation tree and selecting '''Increment Grid''' or ''' Decrement Grid''' from the contextual menu.
* Using the keyboard shortcut {{key|>}} or {{key|<}}.
 
As you “step through” or profile the mesh grid, you can see how the structure is discretized along internal planes of the computational domain.
 
<table>
<tr>
<td> [[Image:Tempo L1 Fig11.png|thumb|left|360px|The XY mesh grid plane.]] </td>
<td> [[Image:Tempo L1 Fig12.png|thumb|left|360px|The YZ mesh grid plane.]] </td>
</tr>
</table>
 
== The FDTD Grid Coordinate System (GCS) ==
 
When your physical structure is discretized using the brick mesh generator, a second coordinate system becomes available to you. The mesh grid coordinate system allows you to specify any location in the computational domain in terms of node indices on the mesh grid. [[EM.Cube]] displays the total number of mesh grid lines of the simulation domain (N<sub>x</sub> × N<sub>y</sub> × N<sub>z</sub>) along the three principal axes on the '''Status Bar'''. Therefore, the number of cells in each direction is one less than the number of grid lines, i.e. (N<sub>x</sub>-1)× (N<sub>y</sub>-1) × (N<sub>z</sub>-1). The lower left front corner of the domain box (Xmin, Ymin, Zmin) becomes the origin of the mesh grid coordinate system (I = 0, J = 0, K = 0). The upper right back corner of the domain box (Xmax, Ymax, Zmax) therefore becomes (I = N<sub>x</sub>-1, J = N<sub>y</sub>-1, K = N<sub>z</sub>-1).
 
[[EM.Cube]] allows you to navigate through the mesh grid and evaluate the grid points individually. Every time you display one of the three mesh grid planes, the "'''Grid Coordinate System (GCS)'''" is automatically activated. On the Status Bar, you will see [[Image:statusgrid.png]] instead of the default [[Image:statusworld.png]]. This means that the current coordinates reported on Status Bar are now expressed in grid coordinate system. The current grid point is displayed by a small white circle on the current mesh grid plane, and it always starts from (I = 0, J = 0, K = 0). Using the keyboard's '''Arrow Keys''', you can move the white circle through the mesh grid plane and read the current node's (I, J, K) indices on the status bar. You can switch back to the "'''World Coordinate System (WCS)'''" or change to the "'''Domain Coordinate System'''" by double-clicking the status bar box that shows the current coordinate system and cycling through the three options. The domain coordinate system is one that establishes its origin at the lower left front corner of the computational domain and measure distances in project unit just like the WCS.
 
<table>
<tr>
<td>
[[Image:FDTD35(1).png|thumb|left|480px|The grid cursor on the XY grid plane and its grid coordinates (I, J, K) displayed on the status bar.]]
</td>
</tr>
</table>
== General Rules of EM.Cube's Surface Mesh Generators ==
Kazem Sabet
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edits