Re: [ff3d-users] Pb in the dx operator

[Stephane Del Pino]

Hi Cécile.

In fact as previously, it is not the dx operator that is wrong. The problem 
comes from the interpolation. Again, there is a problème with the 
interpolation on *non-convex* tetrahedral meshes. I give here more 
explanation. The interpolation (evaluating f(x))process works more or less as 
follows:
- localize x (find the element that contains x)
        1- use an octree that give a good guess T (a tetrahedron that is "near" 
x)
        2- then compute the barycentric coordinates lambda_i of x in T
        3- if lambda_i is negative T is wrong else return T
        4- if T is wrong look into the tetrahedron that shares the face i and 
go to 2
            using the new tetrahedron T
- if T is found evaluate f(x) knowing the values on T else return 0

If the mesh is not convex the problem is that the outer face of T might be a 
boundary of the mesh then the algorithm thinks x is outside...

Having this working for any kind of mesh is a big job... Usual strategy 
consists in adding cells into holes and around the mesh to make it convex: 
this requires a 3d mesher.

In ff3d the octree helps to localize but is not always perfect.

Anyway, I did made a few modifications in the way the octree is built: it is 
no longer based on the centers of the tetrahedra but on the quadrature 
vertices in the tetrahedra and the vertices of the tetrahedra.

Now your *particular* case works. Just update your release, and let me know if 
you still experience some troubles.

I will have a look to a more general implementation of this as soon as 
possible, but I am completely overbooked, so I cannot tell when ...

Best regards,
Stéphane.