IBM Release 1.93 manual The Computational Domain, Symmetry, Unfolded 2N-2 Rows

3.2. The Computational Domain

3.2.1. Symmetry

Many technologically useful devices have a periodic structure. The periodic boundary conditions assumed by POEMS are a natural fit to such structures, which can be simulated very efficiently. This happens automatically if you leave out the absorbers on the sides facing the periodic direction. Almost as many devices exhibit symmetry planes. A domain with a symmetry plane, illuminated symmetrically, will exhibit completely symmetric fields, so no extra information is generated by simulating both halves. Splitting the domain in half down the symmetry boundary can save half the run time and half the memory, while preserving the same level of detail in the results. Domains with more than one symmetry boundary save even more (though this begins to restrict the illumination more severely). POEMS (via support built into TEMPEST, FIDO, and EMPOST) supports symmetrical simulations.

It’s important to visualize the symmetry arrangement correctly, and it isn’t what one might first think: A symmetry plane actually slices right through the centre of the outermost elements. Say the X axis has 100 cells, numbered 0-99. Normally, periodic boundary conditions apply, and cell 0’s neighbours are 1 and 99. If X is a symmetry direction, cell 0’s neighbour is cell 1 on both sides. That is, a 1-block wide layer lying against the symmetry axis has the same effect as a 1-block layer in the middle of the unfolded domain. A 2-block layer against the symmetry axis is equivalent to a 3-block layer down the middle of the unfolded domain.

Unfolded

2N-2 Rows

0 1 2 3 4 5 6 7 8

4

3

2

1

0

1

2

3

4

Actual Domain

N rows

Image Domain N-2 Rows

Next Period

Figure 2.2 Geometry of a symmetry boundary with N=5

31