Re: [Getfem-users] [GetFem-users] Problem in Dof Enumeration and consequ

Dear Simone,

I do not understand well your problem. In GetFEM++, there
is no guaranty of a certain correspondence between dof
enumeration and element indices or vertex indices. The
correspondence can be retrieved via the methods
mf.ind_basic_dof_of_element(cv). Moreover, if I understand
well you compute a mass matrix between a P1 and a
P0 fem. In what sense do you expect a symmetry of this
matrix ?

Note that in the stable releases of Getfem, the order for
scanning the elements for dof enumeration follows a
Cutill-Mc Kee algorithm. By default, this is no longer the
case with the svn version. However, it is quite dangerous
to expect a priori a certain correspondence between dof
indices and mesh element indices.

Best regards,

Yves.

Le 25/10/2016 à 16:55, Simone Di Gregorio a écrit :

Dear GetFem++ users,

I found a problem regarding the resolution of a fem problem. I must solve a 1D-network in terms of pressure and velocity. I have a 1-D network whose mesh structure, made with regions, is like below

BEGIN MESH STRUCTURE DESCRIPTION

CONVEX 0    'GT_PK(1,1)'      0 1
CONVEX 1    'GT_PK(1,1)'      1 2
CONVEX 2    'GT_PK(1,1)'      2 3
CONVEX 3    'GT_PK(1,1)'      4 5
CONVEX 4    'GT_PK(1,1)'      5 6
CONVEX 5    'GT_PK(1,1)'      6 3
CONVEX 6    'GT_PK(1,1)'      3 7
CONVEX 7    'GT_PK(1,1)'      7 8
CONVEX 8    'GT_PK(1,1)'      8 9

END MESH STRUCTURE DESCRIPTION
BEGIN REGION 0
0 1 2
END REGION 0
BEGIN REGION 1
3 4 5
END REGION 1
BEGIN REGION 2
6 7 8
END REGION 2

I use this part of code to obtain mesh_fem:

// pf_Uvi is 'FEM_PK(1,1)' ;
//pf_coefvi is 'FEM_PK(1,0)';
//meshv is the mesh described before;
//nb_branches=3;

for(size_type i=0; i<nb_branches; ++i){

        mesh_fem mf_tmp(meshv);
       mf_tmp.set_finite_element(meshv.region(i).index(), pf_coefv);
       mf_coefvi.emplace_back(mf_tmp);
       mf_tmp.clear();

        mesh_fem mf_tmp1(meshv);
       mf_tmp1.set_finite_element(meshv.region(i).index(), pf_Uv);
       mf_Uvi.emplace_back(mf_tmp1);
       mf_tmp1.clear();
   }

It usually works well for various meshes but in this case in the REGION 1 the dof enumeration of mf_Uvi is wrong, in fact it comes out like:

BEGIN MESH_FEM

QDIM 1
CONVEX 3 'FEM_PK(1,1)'
CONVEX 4 'FEM_PK(1,1)'
CONVEX 5 'FEM_PK(1,1)'
BEGIN DOF_ENUMERATION
3: 3 2
4: 2 0
5: 0 1
END DOF_ENUMERATION
END MESH_FEM

So the Dof enumeration is 3 2   2 0   0 1 while in all other branches is 0 1   1 2   2 3.

While for mf_coefvi in REGION 1 the dof enumeration is in descending order instead of being in ascending order. (So it is 2 1 0 instead of 0 1 2)

BEGIN MESH_FEM

QDIM 1
CONVEX 3 'FEM_PK(1,0)'
CONVEX 4 'FEM_PK(1,0)'
CONVEX 5 'FEM_PK(1,0)'
BEGIN DOF_ENUMERATION
3: 2
4: 1
5: 0
END DOF_ENUMERATION
END MESH_FEM

The problem is not only here, but also if I use this mesh_fem to build the mass matrix, it results to be not symmetric.

//descr.IM_TYPEV='IM_GAUSS1D(6)'

    pintegration_method pim_v = int_method_descriptor(descr.IM_TYPEV);
   mimv.set_integration_method(meshv.convex_index(), pim_v);
    getfem::asm_mass_matrix_param(M, mimv, mf_Uvi[1], mf_coefvi[1], coef, meshv.region(1));

Moreover, also the results of the fem problem are completely wrong.
Instead I noticed that modifying the convex of REGION 1 of the mesh in this way (inverting the node numbers):

CONVEX 3    'GT_PK(1,1)'      3 6
CONVEX 4    'GT_PK(1,1)'      6 5
CONVEX 5    'GT_PK(1,1)'      5 4

I obtain:
- a correct Dof Enumeration:
BEGIN DOF_ENUMERATION
3: 0 1
4: 1 2
5: 2 3
END DOF_ENUMERATION
- a symmetric mass matrix
- a correct solution in terms of velocity
but a wrong solution in terms of pressure (maybe for the boundary conditions).
So I would to know if it is possible to solve the problem and what could be the reason of this error.

Best regards,

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

---------

From:	Simone Di Gregorio
Subject:	Re: [Getfem-users] [GetFem-users] Problem in Dof Enumeration and consequent wrong matrix assembly
Date:	Fri, 28 Oct 2016 12:35:57 +0000