[Gmsh] High-order visualization for hp-FEM solutions

[Beriot, Hadrien]

Hello there,

I have a question regarding the visualization of high-order FEM solutions. I would like to use this feature for visualizing highly oscillatory solutions arising from high-order p-FEM solutions (for instance used in frequency domain electromagnetics and acoustics)? There, by contrast to high-order DG, the difficulty I see is that each element has a unique edge/face orientation, which results pretty much in a different basis definition for each element.

Considering the tetrahedral element for instance, there are usually 6 different possible orientations per face, which yields a total of 1296 different possible basis definitions. In my current understanding, this would require defining 6^4=1296 different "$InterpolationScheme" entities in the input file for gmsh (for the edges shape functions, a workaround can be found by simply multiplying the shape function contribution by +1 or -1 depending on the local edge orientation).

Before I start the actual implementation to make some tests, I would like to know whether


1.       Has anyone tried the high-order visualization feature for viewing 3D p-FEM solutions (integrated Legendre basis)?

2.       Can the current implementation cope with a very large number of interpolation schemes (approx. one per element)? Would it still perform correctly on large models?

Thanks for your help!
Kind regards,

Hadrien



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