# [petsc-dev] Adjacency relations in Sieve and stencils

Chris Eldred chris.eldred at gmail.com
Thu Aug 23 13:39:38 CDT 2012

```Sounds good- I will write the extended topological operators (
star(vertex) \ support(vertex) ; closure(cell) \ cone(cell) and U
cone(support(edge)) ) and let you know if I have questions/run into
issues!

-Chris

On Thu, Aug 23, 2012 at 12:22 PM, Matthew Knepley <knepley at gmail.com> wrote:
> On Thu, Aug 23, 2012 at 12:19 PM, Chris Eldred <chris.eldred at gmail.com>
> wrote:
>>
>> I am working with a 2D unstructured mesh using sieve and I wanted to
>> get some advice on how to determine adjacency relations using the
>> topological operators provided by Sieve (cone, support, closure,
>> star). I have figured out the following:
>>
>> Vertices for a given edge: cone(edge)
>> Cells for a given edge: support(edge)
>>
>> Cells for a given vertex: star(vertex) \ support(vertex)
>> Edges for a given vertex: support(vertex)
>>
>> Edges for a given cell: cone(cell)
>> Vertices for a given cell: closure(cell) \ cone(cell)
>>
>> The set of edges associated with the cells for a given edge: U
>> cone(support(edge)) - ie the union of the cones of the support of the
>> edge
>>
>> Are there other topological operators that more naturally express
>> these relations (especially the ones involving unions or complements)?
>
>
> The only other builtin operations are meet and join. You are correct that
> you
> want to use union there. We could add routines like
>
>   DMComplexGetConeUnion(dm, [p], &unionSize, &unionArray);
>
> but it was not clear that would do anything other than bloat the interface.
> I
> think the best way to procede is to write these convenience routines using
> the lower level primitives, and move them into PETSc if they turn out to be
>
>    Matt
>
>>
>>
>> --
>> Chris Eldred
>> DOE Computational Science Graduate Fellow
>> B.S. Applied Computational Physics, Carnegie Mellon University, 2009
>> chris.eldred at gmail.com
>
>
>
>
> --
> What most experimenters take for granted before they begin their experiments
> is infinitely more interesting than any results to which their experiments
> -- Norbert Wiener

--
Chris Eldred