[petsc-dev] PetscSection

[Tim Tautges]

On 11/10/2012 06:33 PM, Matthew Knepley wrote:
> On Sat, Nov 10, 2012 at 7:14 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:
>> On Sat, Nov 10, 2012 at 5:31 PM, Matthew Knepley <knepley at gmail.com> wrote:
>>>
>>> I was being too pessimistic. You can assign an intermediate node to any
>>> set
>>> of shared vertices, but I am not sure whether you start from the top or
>>> bottom,
>>> and the hard part is preallocation.
>>
>>
>> Hmm, I'm not sure how to do hanging nodes, but for a conforming mesh
>> starting with cell-to-vertex c2v[...]
>>
>> # build inverse map
>> v2c = defaultdict(lambda v:[])
>> for c in cells:
>>    for v in c2v[c]:
>>      v2c[v].append(c)
>>
>> # find common subsets
>> edges = set()
>> c2e = defaultdict(lambda c:set())
>> for v in vertices:
>>    for (v1,c1,v2,c2) in sorted_vertices_appearing_in_exactly_2_cells(v2c[v]);
>>      edges.add((v1,v2))
>>      c2e[c1].add((v1,v2))
>>      c2e[c2].add((v1,v2))
>>
>> # repeat using edges to bound cell-to-face
>> ...
>>
>>
>>
>> The problem with this is that you don't automatically get consistent
>> orientation. If you need to work with basis functions, you need to orient,
>> in which case the ordering produced by the procedure above needs to be
>> fixed.
>>
>> In my opinion, that orientation is critical, such that connectivity without
>> topology is of limited value. The topological dimension and number of
>> vertices is just not sufficient to identify the topology of an element. For
>> example, a hex can be collapsed to 7 vertices via an edge or across the
>> middle of a face.
>
> Definitely, that is much harder than the topology, and where I need specific
> stuff for non-simplices, but it might be possible to use the initial orientation
> of vertices.
>
>      Matt
>

This is a classic compute vs. store problem.  I solve that with the CN (Canonical Numbering) class in MOAB, 
http://trac.mcs.anl.gov/projects/ITAPS/browser/MOAB/trunk/src/moab/CN.hpp.

- tim

> --
> 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
>

-- 
================================================================
"You will keep in perfect peace him whose mind is
   steadfast, because he trusts in you."               Isaiah 26:3

              Tim Tautges            Adjunct Professor, Engr. Physics
          (tautges at engr.wisc.edu)    University of Wisconsin-Madison
          phone: (608) 263-8485      1500 Engineering Dr.
            fax: (608) 263-4499      Madison, WI 53706


-- 
================================================================
"You will keep in perfect peace him whose mind is
   steadfast, because he trusts in you."               Isaiah 26:3

              Tim Tautges            Argonne National Laboratory
          (tautges at mcs.anl.gov)      (telecommuting from UW-Madison)
  phone (gvoice): (608) 354-1459      1500 Engineering Dr.
             fax: (608) 263-4499      Madison, WI 53706