# 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).