Sector 2D and Sector 3D

) and (

) data sets, selected from the submenu, 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 data set first evaluates the input expressions in the source data set, 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 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 list, choose (the default) to use all specified sectors evenly distributed. If you want to use fewer sectors than what you specified in the field, choose a range of sectors using the field (default: 0, for the first sector) and the field (default: the number of sectors, so that you get the same plot as if using ). 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 entered is an even number, select a : (the default) or . For an uneven number of sectors, only rotation is available and it requires no additional user input.

If is selected:

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For, enter and coordinates for the .

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For, enter , , and coordinates for the .

Advanced

Select the check box to create variables for the and the :

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The 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 data set that includes four sectors, for example. The default variable for the sector number is sec1number, where sec1 is the data set node’s tag.

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The evaluate to the coordinate after the transformation (as opposed to x, y, and z, which evaluate to the coordinates in the underlying data set). 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 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 is odd or is selected as the (cyclic symmetry), also enter the . The default is 0.


	Use the azimuthal mode number to control the source data set 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:

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When is selected as the andthe is a multiple of 2 (an even number), select the check box to make the phase of the solution change between consecutive sectors.

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When is selected as the andthe is a multiple of 2 (an even number), select the check box to make the phase change between consecutive sectors. When the s is a multiple of 4, select the check box to make the phase change between consecutive sectors.