Re: E field conversation from Nodal to Edge

[yves . renard]

Dear Egor,

Since Nedelec space is strictly included into the P3 space, I think, you have first to decide the kind of operation you want to do : interpolation or projection.

The interpolation can be done has you described (you can interpolate the P3 fem on the finite element node of the Nedelec FEM, the problem being to perform the scalar product with the right edges).

Concerning the L2 projection, it consists in the assembly of the mass matrix for the Nedelec FEM and the corresponding RHS (Nedelec x P3), then solving the linear system.

Best regards,

Yves

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De: "Egor Vtorushin" <vtorushin@gmail.com>
À: "getfem-users" <getfem-users@nongnu.org>
Envoyé: Vendredi 17 Septembre 2021 10:53:30
Objet: E field conversation from Nodal to Edge

Dear  Yves,
Do you have any hints on how to make a conversation from Nodal mesh fem to Edge mesh fem on the same mesh?

Let we have  ONESIMPLMESH that is 3D mesh with only one 4 vertex simplex(for sake of simplicity)

There are two mesh fems

mfNODAL = gf.MeshFem(ONESIMPLMESH,3)
mfNODAL  .set_fem(gf.Fem("FEM_PK(3,1)"))

and

mfEDGE = gf.MeshFem( ONESIMPLMESH  ,3)
mfEDGE.set_fem(gf.Fem("FEM_NEDELEC(3)"))

Assume we have some three component electric(or else) field defined(evaluated or calculated) in mfNODAL  nodes

In our case it is length of 12 vector - 3 field components in 4 nodes

Now i want to translate this field to mfEDGE mesh fem and gets length of 6 vector- values defined on each edge of the one simplex

I know that it works some basic algebra like for 0-th component of  mfEDGE field E
 E0 = numpy.dot((N0+N1),(PTS[1]-PTS[0]))/2
here (E0 stands for edge and N0,N1 stands for nodal)

But I am interested if there is some way to implement it via generic assembly procedures?
Regards, Egor Vtorushin