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Re: iso-parametric mappings

 

I'm not against changing the xml format. Actually, it would be nice to have a format that is backwards compatible; that way you could ignore the curved information and just use the mesh as straight if you want. That seems do-able.

And then add a local struct to the UFC format that is accessible by the tabulate_tensor routine. This local struct would have the local nonlinear map for each cell and facet in place. I need to look at the UFC manual some more and see how this might work...

- Shawn

On Thu, 14 Aug 2008, Johan Hoffman wrote:


On Wed, 13 Aug 2008, Jed Brown wrote:

On Wed 2008-08-13 17:37, Shawn Walker wrote:
ok, but how would you adjust the xml mesh format?  That should be
figured
out first.  I was thinking one could just add extra data for each cell
that specifies the location of the other control points for the
triangle
sides.  Or maybe it would be better to just supply a finite element
function (2nd order or higher) for the x,y,z coordinates of the mesh
and
do it that way?

I'm a fan of storing coordinates just like any other function, but you
probably want variable order (p-adaptivity) for this since you would
like most elements to have an affine mapping (for efficiency and to
improve the accuracy of the quadrature).

Well, if DOLFIN has p-adaptive functions built into it, then this would
not be a problem.  If it doesn't have it yet, then it could wait.  In the
meantime, I would just have a full P2, or P3 (2nd or 3rd order) function
for all triangles.  And, in addition, provide a boolean function on each
cell that says whether it is straight or not.

I am also interested in curved boundaries. If we do not want to change the
xml format, maybe it would be enough to use a boolean MeshFunction over
the boundary to achieve what you describe?

/Johan








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