# Incorporate new approximated integration methods in *GetFEM++*¶

A perl script automatically incorporates new cubature methods from a description
file. You can see in the directory `cubature`

such description files (with
extension `.IM`

) . For instance for `IM_TETRAHEDRON(5)`

the following file
describes the method:

```
NAME = IM_TETRAHEDRON(5)
N = 3
GEOTRANS = GT_PK(3,1)
NBPT = 4
0, 0.25, 0.25, 0.25, 0.008818342151675485
1, 0.31979362782962991, 0.31979362782962991, 0.31979362782962991, 0.011511367871045398
1, 0.091971078052723033, 0.091971078052723033, 0.091971078052723033, 0.01198951396316977
1, 0.056350832689629156, 0.056350832689629156, 0.44364916731037084, 0.008818342151675485
NBF = 4 IM_TRIANGLE(5)
IM_TRIANGLE(5)
IM_TRIANGLE(5)
IM_TRIANGLE(5)
```

where `NAME`

is the name of the method in *GetFEM++* (constant integer parameter are
allowed), `N`

is the dimension, `GEOTRANS`

describes a valid geometric
transformation of *GetFEM++*. This geometric transformation just defines the reference
element on which the integration method is described. `NBPT`

is the number of
integration node definitions. Integration node definitions include a symmetry
definition such that the total number of integration nodes would be greater than
`NBPT`

.

Composition of the integration node definition:

- an integer: 0 = no symmetry, 1 = full symmetric (x6 for a triangle, x4 for a quadrangle, x24 for a tetrahedron …),
- the
`N`

coordinates of the integration node, - the load.

`NBF`

is the number of faces of the reference element (should
correspond to `GEOTRANS`

). Then follows an already existing
integration method for each face (each on a line). This is necessary
to make integrations on boundaries.

The file format is inspired from [EncyclopCubature].