# 3.5. Spectral solver geometry file format

## Purpose

The geometry file describes a (periodic) volume element on a regular grid.

## Content

A geometry description file contains [optional] information on the
• number of grid points in each direction
• physical size of the box
• homogenization index to be used
• [coordinate origin of the box]
• [maximum microstructure index],
• a list of microstructure indices ordered with x as fastest and z as slowest varying coordinate.
Indices of homogenization and microstructure refer, respectively, to sections within the <homogenization> and <microstructure> part of the material configuration file.

The number of microstructure indices per line is arbitrary (but the total line length should not exceed 8192 characters). In the examples below it corresponds to the number of grid points along the x direction to give a visual clue of the underlying microstructure.

## File compression

• A continuous sequence from N to M can be abbreviated as »N to M«, e.g. »11 to 444« instead of »11 12 13 ... 443 444«.
• N multiples of the same number x can be shortened as »N of x«, e.g., »5 of 4« instead of »4 4 4 4 4«.
• Only a single packing statement is valid per line:
   8 of 3
1 2 2 1 3 3 4 4
4 to 11 

## Examples

### Minimalistic

A minimalistic example as shown in Figure 1 featuring eight regularly shaped grains in a cubic volume with
• 4 x 4 x 4 grid points
• size of 1 x 1 x 1
• using the first homogenization available in material.config

 Figure 1: Volume element containing eight grains of 2 x 2 x 2 voxels each. Darkest blue (not visible) to darkest red span range between microstructure indices 1 to 8.
3   header       # subsequent header lines
grid     a 4    b 4    c 4
size     x 1   y 1   z 1
homogenization   1
1 1 2 2
1 1 2 2
3 3 4 4
3 3 4 4
1 1 2 2
1 1 2 2
3 3 4 4
3 3 4 4
5 5 6 6
5 5 6 6
7 7 8 8
7 7 8 8
5 5 6 6
5 5 6 6
7 7 8 8
7 7 8 8


### Full-fledged

A more complex example with irregularly shaped grains in a hexahedral volume element with
• 22 grains numbered from 1 to 22
• 16 x 32 x 8 grid points
• size of 0.1 x 0.2 x 0.05, i.e., same grid point distance in all three spatial directions
• origin at coordinates (1.0, 0.0, -0.5) and
• using the second homogenization available in material.config
7   header       # number of subsequent header lines
grid     a 16    b 32    c 8
origin   x 1.0   y 0.0   z -0.5
size     x 0.1   y 0.2   z 0.05
# like here!
microstructures 22
homogenization   2
12  12   8   8   8  14  11  11  11  11   7   7   2   2   2   2
12  12  12   8   8  14  11  11  11   3   7   7   7   2   2   2
...


Topic revision: r13 - 01 Apr 2015, MartinDiehl

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