[petsc-users] Reference element in DMPlexComputeCellGeometryAffineFEM

[Matthew Knepley]

On Tue, Nov 8, 2022 at 9:14 PM Blaise Bourdin <bourdin at mcmaster.ca> wrote:

> Hi,
>
> What reference simplex is DMPlexComputeCellGeometryAffineFEM using in 2
> and 3D?
> I am used to computing my shape functions on the unit simplex (vertices at
> the origin and each e_i), but it does not look to be the reference simplex
> in this function:
>
> In 3D, for the unit simplex with vertices at (0,0,0) (1,0,0) (0,1,0)
> (0,0,1) (in this order), I get J = 1 / 2 . [[-1,-1,-1],[1,0,0],[0,0,1]] and
> v0 = [0,0,1]
>
> In 2D, for the unit simplex with vertices at (0,0), (1,0), and (0,1), I
> get J = 1 / 2. I and v0 = [0,0], which does not make any sense to me (I was
> assuming that the 2D reference simplex had vertices at (-1,-1), (1, -1) and
> (-1,1), but if this were the case, v0 would not be 0).
>
> I can build a simple example with meshes consisting only of the unit
> simplex in 2D and 3D if that would help.
>

I need to rewrite the documentation on geometry, but I was waiting until I
rewrite the geometry calculations to fit into libCEED. Toby found a nice
way to express them in BLAS form which I need to push through everything.

I always think of operating on the cell with the first vertex at the origin
(I think it is easier), so I have a xi0 that translates the first vertex
of the reference to the origin, and a v0 that translates the first vertex
of the real cell to the origin. You can see this here


https://gitlab.com/petsc/petsc/-/blob/main/include/petsc/private/petscfeimpl.h#L251

This explains the 2D result. I cannot understand your 3D result, unless the
vertices are in another order.

  Thanks,

      Matt


> Regards,
> Blaise
>
>
>
> —
> Canada Research Chair in Mathematical and Computational Aspects of Solid
> Mechanics (Tier 1)
> Professor, Department of Mathematics & Statistics
> Hamilton Hall room 409A, McMaster University
> 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada
> https://www.math.mcmaster.ca/bourdin | +1 (905) 525 9140 ext. 27243
>
>

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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