dolfin team mailing list archive

[Shawn Walker <walker@xxxxxxxxxxxxxxx>]

On Mon, 25 Aug 2008, Jed Brown wrote:

> For what it's worth, mesh formats like exodusII and VTK accept quadratic
> elements.  They view a quadratic element as a different topology, for
> instance there is VTK_HEXAHEDRON=12 and VTK_QUADRATIC_HEXAHEDRON=25.  Of
> course each of these has a canonical numbering for the nodes.  All
> vertices are kept in one array, then connectivity for each topology
> (either a separate array for each topology or interlaced with a topology
> ID for every element).

Yeah, the quadratic mesh is stored in the standard P2 format, i.e. each 
triangle has 6 nodes associated with it, and they are ordered (locally) in 
the `standard' way.

> I'm not aware of any standard for cubic and higher order meshes (or any
> visualization software that could use it).  In that case, I think the
> most reasonable thing is to store full element connectivity without
> reference to vertices, that is (Region->Face), (Face->Edge),
> (Edge->Vertex) and then store coordinates as a function over this space
> (however you store such things, such as by indexing interior degrees of
> freedom for every element/facet).  Note that there are many more
> coordinates than vertices.

I agree that for visualization, you probably don't need 3rd order or 
higher.  But I can definitely envision PDE problems (discretized) that may 
require it for other reasons.  I am a little confused by what you said for 
storing the coordinates.  So the full element connectivity would still 
require changing MeshTopology?

> Providing a canonical numbering for nodes on say, a cubic hex, requires
> 98 vertices.  Also, the mesh function approach plays nicely with mixed
> order discretization, modal bases, and nonconforming meshes.

how exactly would the mesh function approach work?  Do you mean use 
MeshFunction?

> So it might be reasonable to just implement the quadratic topologies now
> and wait for cubic and higher order since it is a major undertaking to
> do in a flexible manner.

I agree that this should all be tested with quadratic elements first.

- Shawn