Sector 2D and Sector 3D
Use the Sector 2D () and Sector 3D () datasets, selected from the More 2D Datasets and More 3D Datasets submenus, to make it possible to plot the solution for the full geometry while reducing computation time and memory requirements for complex geometries by exploiting sector symmetries. The geometry must be of a type that can be transformed through the use of rotation or reflection (mirroring). Rotation and reflection are only available when using an even number of sectors. It is also possible to invert the phase (change the sign) when rotating or reflecting.
For example, suppose that there are N sectors in a geometry. A Sector dataset first evaluates the input expressions in the source dataset, creates N copies (one for each sector of the geometry), maps and interpolates the data, and transforms the expression components that correspond to vector fields.
Go to Common Results Node Settings for links to information about these sections: Data and Axis Data.
Symmetry
In the Number of sectors field, enter any integer greater than or equal to 2 (the default is 2) to define the number of sectors in the full geometry. From the Sectors to include list, choose All (the default) to use all specified sectors evenly distributed. If you want to use fewer sectors than what you specified in the Number of sectors field, choose a range of sectors using the Start sector field (default: 0, for the first sector) and the Number of sectors to include field (default: the number of sectors, so that you get the same plot as if using All). You can use these settings to only plot a fraction of the sectors in order to see the solution inside of the resulting geometry.
When the Number of sectors entered is an even number, select a Transformation: Rotation (the default) or Rotation and reflection. For an uneven number of sectors, only rotation is available and it requires no additional user input.
If Rotation and reflection is selected:
•
For Sector 2D, enter x and y coordinates for the Direction of reflection axis.
•
For Sector 3D, enter x, y, and z coordinates for the Radial direction of reflection plane.
Advanced
Select the Define variables check box to create variables for the Sector number and the Space variables:
•
The Sector number is an integer number from 0 to the number of sectors minus 1. Each sector has a unique sector number: 0, 1, 2, and 3 for a sector dataset that includes four sectors, for example. The default variable for the sector number is sec1number, where sec1 is the dataset node’s tag.
•
The Space variables evaluate to the coordinate after the transformation (as opposed to x, y, and z, which evaluate to the coordinates in the underlying dataset). The default variable names (the number of which are based on space dimension) are sec1x for the x coordinate, sec1y for the y coordinate, and sec1z for the z coordinate.
When the Define variables check box is selected, the input expression is enabled once for each sector, something that increases evaluation time by roughly a factor of the number of sectors (N). If the input expression being evaluated contains any of the space variables, then this evaluated mode is enabled automatically.
Azimuthal Mode Number
When the Number of sectors is odd or Rotation is selected as the Transformation (cyclic symmetry), also enter the Azimuthal mode number as an integer. The default is 0. You can also use a mode number that is defined as a parameter or a variable.
Use the azimuthal mode number to control the source dataset and evaluate it with different phases for the different sectors. If the mode number is k, then the phase shifts with −2π ik/N for sector i.
Invert Phase When Rotating and Invert Phase When Reflecting
These check boxes are available in various combinations as follows:
•
When Rotation is selected as the Transformation and the Number of sectors is a multiple of 2 (an even number), select the Invert phase when rotating check box to make the phase of the solution change between consecutive sectors.
•
When Rotation and Reflection is selected as the Transformation and the Number of sectors is a multiple of 2 (an even number), select the Invert phase when reflecting check box to make the phase change between consecutive sectors. When the Number of sectors is a multiple of 4, select the Invert phase when rotating check box to make the phase change between consecutive sectors.