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

[Chris Eldred]

On Wed, Jul 25, 2012 at 12:30 PM, Matthew Knepley <knepley at gmail.com> wrote:

> 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 missed the little section on ConeOrientation in the DM man pages- that
makes perfect sense. I could just traverse the arrays in each cell using
the ConeOrientation and the association would be preserved.


> 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
>



-- 
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
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