[petsc-users] Input arguments of DMPlexCreateFromDAG

[Cedric Doucet]

Hello, 

DMPlexInterpolate is very interesting! 
Is it slow? 

If I want to call DMplexInterpolate, just after DMPlexCreateFromDAG call, for the example of two triangles sharing an edge, I only have to specify cells and vertices like this in DMPlexCreateFromDAG: 

PetscInt numPoints[3] = {4, 0, 2}; 
PetscInt coneSize[11] = {3, 3, 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}; 

and let cones and coneOrientations be empty? 

Cédric 

----- Mail original -----

> De: "Matthew Knepley" <knepley at gmail.com>
> À: "Cedric Doucet" <cedric.doucet at inria.fr>
> Cc: petsc-users at mcs.anl.gov
> Envoyé: Vendredi 31 Janvier 2014 12:21:40
> Objet: Re: [petsc-users] Input arguments of DMPlexCreateFromDAG

> 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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