Re: [Getfem-users] Getfem enumeration of DOFs in XFEM

[Yves Renard]

Dear Bianca,

The answer is not so easy. The implementation of Xfem in Getfem is quite general and support the multi-level-sets case. Thi means that an element can be cut by an arbitrary number of level-sets. A finite element shape function whose support is (completely) cut by n level-sets will be duplicated the necessary number of time (max 2^n). It corresponds to Hansbo's strategy but generalized to the multi-level-sets case. In the case of a unique level-set, each shape function whose support is completely cut by the level-set is duplicated into two, each degree of freedom representing the finite element field on one side of the level-set (this means that there is not the standard degree of freedom and the enriched one). Of course, this is equivalent to the standard Xfem strategy and a linear combination of the two degrees of freedom can give you the non-enriched and enriched degree of freedom of the standard Xfem.

The information for each dof that it is enriched or not can be retreived by
pdof_description pdd = mf.fem_of_element(cv)->dof_types()[i];
where i is the local (to the element) dof number and pdd is a pointer on a structure describing the type of dof (see the file src/getfem_fem.cc)
The function
 dof_xfem_index(pdd)
will return the index of enrichement (0 : non eneriched, n : first zone, n+1 : second zone ...) where n is typically 1000.


Concerning tip enrichement, this is taken into account in a very different way. It uses a global mesh_fem (i.e. not really linked to a mesh), see src/getfem/getfem_mesh_fem_global_function.h and a mesh_fem_sum object.
This is a quite tricky part of Getfem which would have to be optimized.

Similarly, such dofs can be detected since they are declared as "global dofs", see getfem_mesh_fem_global_functions.



Best regards,

Yves.





Le 24/06/2015 18:39, Bianca Giovanardi a écrit :

Dear Yves,

I am a PhD student at Politecnico di Milano and I am using Getfem++ for the numerical simulations involved in my thesis about crack propagation.

I have compiled and tested crack.cc. To perform some post processing computations on the displacement, I need to know how the degrees of freedom are enumerated in the vector of the enriched displacement.

I have understood that the even elements of the vector correspond to an x component and the odd ones correspond to a y component, but it is not clear to me in which order the non enriched DOFs, the Heaviside enriched DOFs and the tip enriched DOFs are set.

I hope I managed to explain myself and that you can help me.

I thank you very much for your time,

Bianca Giovanardi

MOX - Modeling and Scientific Computing

Department of Mathematics "Francesco Brioschi"

Politecnico di Milano

Via Bonardi 9, 20133 Milano, Italy

_______________________________________________
Getfem-users mailing list
address@hidden
https://mail.gna.org/listinfo/getfem-users

-- 

  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
  Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE
  http://math.univ-lyon1.fr/~renard

---------