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[Anders Logg <logg@xxxxxxxxx>]

Yes, and I'm sorry for the inconvenience. I did suggest to use what we
had before (as the common convention for FFC and SyFi) but something
else came up which was simply better. It's less ad hoc and it extends
to numbering of entities on n-D simplices, quads and hex elements.

It looks like one would only need to make the following updates in
shapes.py in FIAT:

triangle_edges = { 0 : ( 1 , 2 ) , \
                   1 : ( 0 , 2 ) , \
                   2 : ( 0 , 1 ) }

tetrahedron_edges = { 0 : ( 2 , 3 ) , \
                      1 : ( 1 , 3 ) , \
                      2 : ( 1 , 2 ) , \
                      3 : ( 0 , 3 ) , \
                      4 : ( 0 , 2 ) , \
                      5 : ( 0 , 1 ) }

tetrahedron_faces = { 0 : ( 1 , 2 , 3 ) , \
                      1 : ( 0 , 2 , 3 ) , \
                      2 : ( 0 , 1 , 3 ) , \
                      3 : ( 0 , 1 , 2 ) }

If I make these changes in FIAT, everything works fine. I get
convergence for q = 1, 2, 3 in both 2D and 3D. (Didn't try higher
degree but I'm sure it works.)

If changing this in FIAT will be problematic for Sundance, perhaps you
could add a little hook for setting the values listed above?

I could live with an extra call to set the values until you've talked
Kevin into making the corresponding updates to Sundance... :-)

/Anders


On Sat, Jun 09, 2007 at 08:36:24PM +0200, Robert Kirby wrote:
> I don't mind it being something different that makes sense, except that I
> thought we had agreed on what is there a year or two ago and changing would
> also require some small changes in Sundance also.
> 
> Rob
> 
> 
> 
> On 6/9/07, Anders Logg <logg@xxxxxxxxx> wrote:
> 
>     We're having problems with getting higher order Lagrange converge in
>     3D and I think we've tracked it down to FFC/DOLFIN and FIAT not
>     agreeing on the numbering of edges on the reference tetrahedron.
> 
>     Here's the numbering that FIAT seems to use (listed as the incident
>     vertices of each edge):
> 
>       e0 = (1, 2)
>       e1 = (0, 2)
>       e2 = (0, 1)
>       e3 = (0, 3)
>       e4 = (1, 3)
>       e5 = (2, 3)
> 
>     The UFC convention wants the edges sorted by their non-incident
>     vertices so we would like to have
> 
>       e0 = (2, 3)    non-incident to (0, 1)
>       e1 = (1, 3)    non-incident to (0, 2)
>       e2 = (1, 2)    non-incident to (0, 3)
>       e3 = (0, 3)    non-incident to (1, 2)
>       e4 = (0, 2)    non-incident to (1, 3)
>       e5 = (0, 1)    non-incident to (2, 3)
> 
>     The ordering convention is described in detail in the FFC, DOLFIN and
>     UFC manuals and it's based on what Arnold, Falk, Winther use for
>     numbering sub simplices in arbitrary dimensions.
> 
>     The basic principle is that for each entity, you look at its
>     *non-incident* vertices and sort the entities lexicographically by
>     those (sorted) tuples of non-incident vertices. So the first edge
>     of a tetrahedron would then be the edge that is non-incident to
>     vertices 0 and 1. This is pretty neat since it also specialized to the
>     familiar numbering of edges in 2D and faces in 3D, so that edge (or
>     face) i is the edge (or face) opposite to vertex i.
> 
>     Would it be possible to change the edge numbering for tets in FIAT to
>     follow this convention?
> 
>     (Ideally, I'd also like to have the vertices at (0, 0, 0) - (1, 0, 0)
>     - (0, 1, 0) - (0, 0, 1) rather than (-1, -1, 0) etc but we already
>     handle this in FFC by scaling all the basis functions and
>     derivatives.)
> 
>     /Anders
>     _______________________________________________
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> 
> 

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