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

[Noah Reddell]

 I am trying to setup a visualization solution for my research code which produces structured, nodal data, based on a discontinuous Galerkin solution method for fluid equations.

The domain is either 2D, 3D, 4D, 5D, or 6D.  Yes, greater than 3D, because my primary model produces kinetic data sampled in phase space (3D position and 3D velocity).
The domain is discretized by elements that are generalized N-dimensional quadrilaterals. (quadrilaterals, hexahedrals, etc.) organized in a block-structured mesh.
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.
The solution is multi-valued at faces where two elements are adjacent and I want the visualization to well-capture the surface discontinuity.
My mesh and nodal data are both stored in HDF5 files, with some flexibility to modify formatting.


I spent some time reviewing the ParaView user guide and document for plugin reader development and now have a few questions before I can proceed.

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.  That’s not surprising but seems to suggest I will have to write a custom reader plugin to access my 4D+data.  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?

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?  In this way, the real elements are still adjacent, but their vertices / nodes can be assigned different vales.  One concern I have is the hidden element would have zero-volume.  I’d hate to develop that design and then have some ParaView internal function break due to a divide by zero error or something similar.  Another problem area might be plotting stream tubes from the data set.

Lastly, for the high order visualization, I thinking the most straight forward approach is to interpolate my structured high order elements  into a new fine mesh of structured linear elements.  That should be good enough.  On this forum, 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?

Here’s an old thread that brought up the same basic goals as mine: http://www.paraview.org/pipermail/paraview/2006-October/003899.html
(The numerical scheme and element types are not exactly what I’m working on, but the ideas are similar.)

I really appreciate any feedback.

Best Regards,

Noah Reddell
University of Washington

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