[petsc-users] sieve-dev Data shared between points in a Sieve DAG

[Matthew Knepley]

On Wed, Jul 25, 2012 at 1:07 PM, Chris Eldred <chris.eldred at gmail.com>wrote:

> Lets consider the mesh from "Flexible Representation of Computational
> Meshes" on the LHS of figure 2. (0,1) (0,2) (0,3) and (0,4) are vertices;
> (0,5), (0,6), (0,7), (0,8) and (0,9) are edges; (0,10) and (0,11) are
> cells. My field would be defined as (for example):
>
> field ( (0,5) ; (0,10) ) = 1.0
> field ( (0,6) ; (0,10) ) = 2.0
> field ( (0,7) ; (0,11) ) = 1.3
> etc.
>
> Does that make sense?
>

Oh, are you wanting something like DG? The tying of data values to mesh
points is primarily to indicate
sharing of values. If you have something like DG, I would initially do
something like you did, which is
assign all the variables to the cell since they are not shared. Since the
cone is always oriented, the
association between edges and values would be guaranteed.

I have thought about another way to do this, but I don't think its any
easier. You could instead associate
2 values with an edge, one for one side and the other for another. You can
then look at the coneOrientation
for that edge in the cell to know which value to choose for the cell. I am
not sure this is easier, but it does
facilitate communication of the "other" value for cells with neighbors on
other processes.

    Matt


> On Wed, Jul 25, 2012 at 11:57 AM, Matthew Knepley <knepley at gmail.com>wrote:
>
>> On Wed, Jul 25, 2012 at 12:52 PM, Chris Eldred <chris.eldred at gmail.com>wrote:
>>
>>> The closure operation makes sense, but what I want is something a little
>>> different.
>>>
>>> I have a field that is defined as follows:
>>> field(edge,cell) = blah
>>> ie it really lives on the union of cells and edges (or vertex/edges,
>>> cells/vertexs, etc.)
>>>
>>
>> We need to make the language more precise. The union of the cell and edge
>> is what
>> closure would give you.
>>
>>
>>> Is this something that can be defined using DMComplex and Sections?
>>
>>
>> I cannot understand from this explanation. Can you give a small example?
>>
>>   Thanks,
>>
>>      Matt
>>
>>
>>> On Wed, Jul 25, 2012 at 11:39 AM, Matthew Knepley <knepley at gmail.com>wrote:
>>>
>>>> On Wed, Jul 25, 2012 at 11:23 AM, Chris Eldred <chris.eldred at gmail.com>wrote:
>>>>
>>>>> I was wondering if it was possible to have fields that are shared
>>>>> between points in a sieve DAG:
>>>>>
>>>>> For example, I would like to have data that is connected to both an
>>>>> edge and a cell (instead of just tied to a Section). Consider a cell with
>>>>> three edges (ie a triangular cell).
>>>>>
>>>>> Before I was just using a length 3 array attached to the cell with the
>>>>> convention that the ordering of the array matched the ordering of the edge
>>>>> list associated with the cell. Now, I would like an implementation that
>>>>> does not assume anything about the ordering of the edge list (since I am
>>>>> getting that from cones/supports).
>>>>>
>>>>
>>>> I think what you want is the Closure operation. The closure of a cell
>>>> will give you all the unknowns on its edges and vertices.
>>>> Does that make sense?
>>>>
>>>>   Thanks,
>>>>
>>>>      Matt
>>>>
>>>>
>>>>> Thanks,
>>>>> -Chris Eldred
>>>>>
>>>>> --
>>>>> Chris Eldred
>>>>> DOE Computational Science Graduate Fellow
>>>>> Graduate Student, Atmospheric Science, Colorado State University
>>>>> 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 lead.
>>>> -- Norbert Wiener
>>>>
>>>
>>>
>>>
>>> --
>>> Chris Eldred
>>> DOE Computational Science Graduate Fellow
>>> Graduate Student, Atmospheric Science, Colorado State University
>>> 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 lead.
>> -- Norbert Wiener
>>
>
>
>
> --
> Chris Eldred
> DOE Computational Science Graduate Fellow
> Graduate Student, Atmospheric Science, Colorado State University
> 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 lead.
-- Norbert Wiener
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