[Paraview] Seeking advice for high-order and high-dimensional discontinuous Galerkin data

[Noah Reddell]

Thank you for the feedback David.
Another developer and I are going to forge ahead and see what sort of prototype we can get working.

For simplicity, we will avoid the composite data sets for now — the supposed approach to use AMR-like data sets to represent each actual high order element.  In general, our simulations produce somewhere around 4-9 samples per element axis.  This falls mostly below your gut threshold for when composite data sets might be effective.  This does spur a curiosity though.  A refined AMR region adjacent to a course region could produce multi-valued nodal data or cell-centered data.  Is there anything to learn from ParaView’s treatment of multi-valued data at AMR region faces?

Since you say that zero-volume virtual-elements could be problematic, I propose a simpler approach along the same idea.  Interpolate the high-order element solution to a structured mesh, where the structured mesh samples arbitrarily close-to, but not on the original element face.  So, where the original mesh has high order elements with discontinuous solutions at the element faces, the new mesh would have structured nodal values all inside the original elements.  The new mesh might span from [1% to 99%] along each element face dimension.  This would leave one cell with about 2% element width that could have a high gradient connecting two ‘element’ regions.

Does that make sense?  If not, and assuming the list allows attachments, I could draw a picture.

-Noah


On Apr 11, 2014, at 1:02 PM, David Thompson <david.thompson at kitware.com> wrote:

> Hi Noah,
> 
>> ...
>> 	• The solution on any given element is smooth, represented by arbitrary order polynomials and sampled at surface and interior node locations.  I tend to use high order elements compared to typical practice, i.e. 7th, 8th, 9th-order. I’d like the visualization to capture some of the element’s internal solution structure rather than just a linear interpolation between element vertices.
> 
> If you are dealing with meshes where regular sampling of higher order elements is feasible and the number of samples per element per axis is high (>8?), you might consider using composite datasets (AMR or multiblock datasets), with each block holding image data for a single element.
> 
>> 	• The solution is multi-valued at faces where two elements are adjacent and I want the visualization to well-capture the surface discontinuity.
> 
> That can be troublesome with precisely coincident grid points since rendering just those boundaries will exhibit z-fighting. If you isocontour, you will see cracks at element boundaries which reflect discontinuities. A better understanding of what you intend to visualize might help decide how to organize the data.
> 
>> ... Obviously ParaView is focused on 2D and 3D data. The underlying VTK looks to only handle up to 3D vertex position vectors, for example.  My takeaway from this, is it is not possible to describe a 4D or higher mesh to ParaView directly.
> 
> No.
> 
>> ... My survey of the documentation makes me think that I’ll be able to provide parameters to the reader plugin that control the dataset.  For example, specify what dimensions to slice and where to slice.  I suppose I need to similarly parameterize the load of the mesh.  Does this sound like a workable approach?
> 
> Yes. You may also want to take a look at http://www.vtk.org/Wiki/VTK/InSituDataStructures and vtkTypedDataArray as a way to provide 3-d point coordinates from a higher-dimensional array (and the remaining dimensions as other independent arrays). But it's unclear to me -- assuming you regularly sample phase space the same way you sample positional space -- how you would handle places where the projection to a subset of those dimensions resulted in coincident elements in the projected space.
> 
>> For the data discontinuities at element faces, I’ve seen discussions in this forum that suggest unstructured grids with duplicated/co-located vertices allows for assigning two different data values at the same physical location.  Since I am working with structured grids and data, I’m wondering if a different technique might work.  How about inserting zero-volume collapsed elements between each real element?
> 
> I think this would be problematic for many VTK filters.
> 
>> Lastly, for the high order visualization, ... the most straight forward approach is to interpolate my structured high order elements... vtkBridgeDataSet has been mentioned as a possible approach but requiring much development effort.  That was several years ago.  Has there been any progress by others with similar high-order or spectral data sets?
> 
> Sadly, no. Although we have had a lot of interest from academia, there haven't been paying customers for this.
> 
> 	David
> 

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