[MOAB-dev] Compute volume and surface areas of dual mesh

[Tim Tautges]

I think the only way currently to do that would be to actually form the dual, though, it might be easy enough to write 
code to compute the dual volume on the fly (would involve assembling the contributions for each tet connected to each 
vertex based on positions computed from centroids).  Most efficient would probably be caching the centroids as tags on 
the entities.

- tim

On 09/16/2011 09:51 AM, Jed Brown wrote:
> On Fri, Sep 16, 2011 at 14:40, Iulian Grindeanu <iulian at mcs.anl.gov
> <mailto:iulian at mcs.anl.gov>> wrote:
>
>     Hello,
>
>     What is the dual of a tetrahedral mesh?
>     If the mesh is Delaunay, one dual is the Voronoi partition.
>     If the mesh is arbitrary, I don't think there is a unique partition
>     that can be defined.
>     You can always define a voronoi partition, but it will not be
>     necessarily dual to initial tetra mesh.
>
>
> Yeah, I'm thinking of the Delaunay/Voronoi dual (vertices become dual
> centers). I think the initial mesh will typically be Delaunay. The issue
> is that vertex-centered finite volume discretizations don't need cell
> connectivity, they only need to know the volumes of dual cells (primal
> vertices) and the surface area of dual faces (primal edges).
>
> In this case, I already have tetrahedral meshes and just want to compute
> the sizes of these dual volumes. (I don't need the dual volumes
> themselves, just the sizes.

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              Tim Tautges            Argonne National Laboratory
          (tautges at mcs.anl.gov)      (telecommuting from UW-Madison)
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