On Tue, 16 Feb 2010, Rahul Sampath wrote:

>  HEX8: 7        6
>        o--------o
>       /:       /|
>      / :      / |
>   4 /  :   5 /  |
>    o--------o   |
>    |   o....|...o 2
>    |  .3    |  /
>    | .      | /
>    |.       |/
>    o--------o
>    0        1
>
>     TET4:
>        3
>        o
>       /|\
>      / | \
>     /  |  \
>  0 o...|...o 2
>     \  |  /
>      \ | /
>       \|/
>        o
>        1
>
> However, you have not shown the coordinate axes. I need to know the following:
> 1) The relationship between the local coordinate system and the local
> node numbering scheme. For  example, In Hex8 whether the edge 0-1 is
> parallel to the local xi or eta axes.
>
> 2) The relationship between the physical global coordinate system and
> the local coordinate system.
>
> I believe you must already be using some convention for both to be
> able to compute the Jacobian of the transformation. It would be very
> helpful if you could tell me where I can find this information.

To the best of my recollection:

For triangles and tets, the nodes are at (0,0,0), (1,0,0), (0,1,0),
(0,0,1) in master coordinates

For tensor product elements, the geometry is [-1,1]^d and the edges
are 0-1:xi, 0-3:eta, 0-4:zeta

For pyramids, the peak is at (0,0,1) and the base is the same as a
quad.

Prisms are the tensor product of a triangle and an edge, with the
triangle at zeta=-1 given the lower local node numbers.

I'm afraid that the only place where you can find this information
solidly may be implicitly in the fe_lagrange*.C code, though; I'm not
sure we've got it cleanly documented.  If you'd like to add such
documentation, a patch (in ASCII so we can put it in the headers)
would be appreciated.
---
Roy

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