[petsc-users] Input arguments of DMPlexCreateFromDAG

[Matthew Knepley]

On Fri, Jan 31, 2014 at 3:23 AM, Cedric Doucet <cedric.doucet at inria.fr>wrote:

>
> Thank you for your answer.
> I understand well the reason why coneSize begins with faces of cells and
> vertices first.
> However, I am not sure to understand how cone points are numbered in the
> definition of <start>.
> For example, in CreateSimplex2D in ex5.c (two triangles sharing an edge),
> we have:
>
> PetscInt    numPoints[3]             = {4, 5, 2};
> PetscInt    coneSize[11]              = {3, 3, 0, 0, 0, 0, 2, 2, 2, 2, 2};
> PetscInt    cones[16]                   = {6, 7, 8,  9, 7, 10,  2, 3,  3,
> 4,  4, 2,  5, 4,  3, 5};
> PetscInt    coneOrientations[16] = {0, 0, 0,  0, -2, 0,  0, 0,  0, 0,  0,
> 0,  0, 0,  0, 0};
> PetscScalar vertexCoords[8]      = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5,
> 0.5};
>
> The fact that coneOrientations[4] equals -2 means that edge cones[4]=7
> must be oriented in reverse order starting at vertex 1.
> However, edge 7 is defined by vertices (3,4). Does it mean that a local
> numbering is used here: (3,4)~(v0,v1)?
>

Yes, exactly the numbering from cones[8-9].


> In algebraic topology, a convenient way to orient simplices is to number
> their vertices in ascendant order.
> For example, an edge (i,j) is oriented so that i<j, a face (i,j,k) is
> oriented so that i<j<k, etc.
> Can we adopt the same convention here and does it simplify something?
>

No, because we do not have exclusively simplices.

You can simplify by only specifying cells and vertices, which need no
orientations, and then calling DMPlexInterpolate().

  Matt


> Best regards,
>
> Cédric Doucet
>
>
> ------------------------------
>
> *De: *"Matthew Knepley" <knepley at gmail.com>
> *À: *"Cedric Doucet" <cedric.doucet at inria.fr>
> *Cc: *petsc-users at mcs.anl.gov
> *Envoyé: *Jeudi 30 Janvier 2014 19:26:36
> *Objet: *Re: [petsc-users] Input arguments of DMPlexCreateFromDAG
>
> On Thu, Jan 30, 2014 at 12:19 PM, Cedric Doucet <cedric.doucet at inria.fr>wrote:
>
>> Hello,
>> I tried to use DMPlexCreateFromDAG function to create a DM structure from
>> a hybrid mesh.
>> To understand how it works, I look at ex5.c file.
>> Unfortunately, there are some things that I do not understand.
>> 1. Why does coneSize lists faces of cells first, then faces of vertices
>> and finally faces of edges (in 2D)? Listing faces of vertices, then faces
>> of edges and finally faces of cells is not simpler?
>>
>
> This is really about what order you number points. I wanted to support
> meshes with just cells and vertices, as well as
> those with face and edges. I also wanted to be able to convert between
> them. Thus it made sense to leave the cell
> and vertex numbers invariant under this change. I still think this is the
> best pragmatic alternative.
>
>
>> 2  What does coneOrientations contain? For two counterclockwise oriented
>> triangles sharing an edge e={v0,v1}, I understand that {v0,v1} is the right
>> oriented edge for the second triangle (and e for the first one) but what
>> is the meaning of value -2? I read that it is -(o+1) with o=1 but why does
>> o equal 1 in this case?
>>
>
> Right now, orientation o = <sign><start> means:
>
>   <sign>: + means traverse in cone order
>                  - means traverse in the reverse of cone order
>
>   <start>: cone point to start iteration on
>                 if <sign> is -, then start on point -(<start>+1)
>
> Thus -2 means start on point 1 and go in reverse order, so
> for an edge that would be {1, 0} which is what you want.
>
> What we should really have is <start> identify a group element from the
> symmetry
> group of the point, and <sign> indicate inversion. However, that will be a
> big rewrite
> and needs to be motivated by applications.
>
>    Matt
>
> Thank you very much for your help!
>> Best regards,
>> Cédric Doucet
>>
>>
>
>
> --
> 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
>
>
>


-- 
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
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