# Integ module¶

## Description¶

The CUBATURE module gives access to the numerical integration methods on
reference elements. In fact it does not only contain some cubature formulas
because it also give access to some exact integration methods. However, the exact
integration methods are only usable for polynomial element and affine geometric
transformations. This explain why exact integration methods are not widely used.
The description of cubature formulas is done either directly in the file
`getfem_integration.h`

or via a description file in the directory
`cubature`

of *GetFEM*. The addition of new cubature formulas is then very simple,
it suffices to reference the element on which it is defined and the list of Gauss
points in a file and add it to this directory. Additionally, In order to
integrate terms defined on a boundary of a domain, the description should also
contains the reference to a method of same order on each face of the element.

## Files¶

File(s) | Description |
---|---|

`getfem_integration.h` and `getfem_integration.cc` and `getfem_integration_composite.cc` |
Structure of integration methods, basic integration methods, product of integration method and composite methods. |

`getfem_im_list.h` |
file generated by `cubature/make_getfem_list` with the integration methods defined in cubature directory. This gives the possibility to define a new integration method just listing the Gauss points and weigth in a text file. |

## State¶

This module meets the present needs for the project and is considered as stabilized. The list of available cubature formulas is given in Appendix B. Cubature method list.

## Perspectives¶

No change needed for the moment. An effort could be done on the documentation to describe completely how to add a new cubature formula (format of descritption files).