[vtkusers] [EXTERNAL] Higher order elements in VTU files

[David Thompson]

Hi Mikael,

> Hi. I'm a developer for a finite element code ...
> I found both in vtkCellType.h  and on
> http://www.paraview.org/Wiki/ParaView/Users_Guide/VTK_Data_Model
> a lists many of the types i would wish to find, but they are not
> documented in the file format guide.

The bi- and tri-quadratic elements were implemented by Soeren Gebbert  
and can be members of a vtkUnstructuredGrid. The vtkExodusIIReader  
will certainly read them and I believe the legacy and XML readers also  
handle them properly.

> In fact, all cell types from VTK_PARAMETRIC_* and VTK_HIGHER_* doesn't
> seem to be implemented.

NURBS are not implemented. The VTK_HIGHER_* types are for use with the  
vtkGenericDataSet mesh format, not vtkUnstructuredGrids. The  
vtkGenericDataSet mesh was meant to serve as a way for novel PDE  
discretization techniques to be rendered with VTK -- without VTK  
having to understand the interpolation strategy or choose a sampling  
strategy. Thus, the class serves as an "adaptor" between visualization  
code and the FE solver providing the interpolation functions.  
Subclasses of vtkGenericAdaptorCell were intended to provide their own  
linearized approximations for rendering. However, the filters for this  
mesh type are not as well tested as those that work with unstructured  
grids.

> I can only imagine how hard it would be to try and fit general
> parametric functions into the same procedure, as the nodes can have
> arbitrary positions in the mapped coordinate system.
>
> 1. Are they just placeholders?

As above, they are intended for use by cells in a vtkGenericDataSet.  
However, there are not currently open-sourced, higher-order finite  
elements.

> 2. Is there any plan to implement these parametric and higher order  
> elements?

Kitware has written one set of "adaptors" for an existing finite  
element package and Sandia developed another, but neither are open- 
source at the moment. The Sandia version was hampered by the fact that  
there were not robust polynomial system solvers at the time (which are  
needed to identify the critical points of interpolants, in turn needed  
to guarantee true maxima and minima are shown).

> 3. Can I export the bi-quadratic and tri-quadratic element types to
> *.vtu files (even though they are not listed in file format
> documentation)? i.e. the file format documentation should probably be
> updated.

Yes, the documentation should probably be updated. I believe the  
documentation of the various cell types includes the ordering expected  
for the volume-, face-, and edge-centered nodes in a vtkCellArray.

	Regards,
	David