dolfin team mailing list archive

[Martin Sandve Alnæs <martinal@xxxxxxxxx>]

On Thu, Apr 2, 2009 at 5:12 PM, Shawn Walker <walker@xxxxxxxxxxxxxxx> wrote:
> Hello all.
>
> I have finally got some time to put in (at least the first stage) the
> higher order mesh stuff for triangles
> mapped with P2 lagrange elements. Just to remind you, the agreement that
> we came up with was this:
>
> 1. The local mapping for each element is independent of whatever finite
> elements you are using.  Thus, there
> should be a completely different description of the mapping.
>
> 2. This info will be stored in MeshGeometry with extra data structures.
>
> 3. The info to store is (i) all the higher order vertex position data, and
> (ii) the `DoFmap' for your
> particular map.  Storing the extra vertex data is just like storing the
> usual 3 triangle coordinates.
>
> 4. Eventually, for computing the local finite element matrices, there just
> needs to be a short subroutine
> that returns the higher order vertex data (for a specific cell) to be used
> by, say, the code generated by
> FFC.

Just two minor additional remarks:
- The code generated by FFC won't have access to a subroutine from DOLFIN.
Therefore, this data (for a specific cell) must be placed in the ufc::cell
datastructure which can be extended with additional data fields if needed
and additional numbering conventions for the new local data if needed.

- The new form language UFL, which will be introduced officially very soon,
has very basic support for the input side of this by using
Cell("triangle", degree)
instead of "triangle" as input to FiniteElement. Of course, the form compilers
do not yet support this. If degree is not enough, more variables can easily
be added there.

> My question is about the dofmap.  It is certainly reasonable to store it
> similarly to the vertex data.  But
> there is a problem if the mesh is locally refined.  It seems like it will
> be a pain to modify this data
> structure.  Any suggestions for this?
>
> Remember, we do NOT want to use a function space here.  This was already
> discussed!
>
> - Shawn
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