How can I identify if a mesh is periodic from the basis name?

[JustinPrivitera]

Hello, VisIt developer here. Is there a way to tell if an mfem mesh is periodic from the grid function basis name?

These are periodic: L2_T1_3D_P1, L2_T1_2D_P1
These are not: H1_3D_P2, L2_2D_P3, L2_T2_3D_P1

Is it the T1? The P1?

[pazner]

All periodic MFEM meshes will use L2 spaces (so the prefix will be L2), but not all meshes with L2 spaces will be periodic. I don't know of any way to tell if a mesh is actually periodic (in any case, what about a mesh that is periodic only in one dimension vs. two dimensions, etc.?).

[JustinPrivitera]

This is how we test in VisIt if something is periodic:

    if (mesh && 
        mesh->GetNodes() && 
        mesh->GetNodes()->FESpace() &&
        mesh->GetNodes()->FESpace()->FEColl() &&
        dynamic_cast<const L2_FECollection *>(mesh->GetNodes()->FESpace()->FEColl()))
    {
        // Check if the mesh is periodic.
        AVT_MFEM_INFO("High Order Mesh is periodic; falling back to Legacy LOR.");
        return LegacyRefineMeshToVTK(mesh, domain, lod);
    }

[pazner]

I think the best option for detecting periodicity is just to check if the space is L2, which may have false positives, but will never have false negatives.

If you just need the physical coordinates of the nodes, that is easy to get with MFEM (even for periodic meshes).

What seems to make this tricky is that MFEM handles periodic meshes by combining/merging vertices. For example, a periodic line segment actually only has one endpoint vertex, rather than two endpoint vertices. So if you are working directly with the mesh vertices, things will get tangled like you see above.

[JustinPrivitera]

We discussed an algorithm to do exactly that back in 2022. Tzanio said this:

For the case of LOR periodic mesh, I can imagine an algorithm like this:

• initialize vertex coordinates to nans
• for each element:
• use the element nodes to get vertex coordinates
• for each vertex:
• if the previous value was nan or round-off close to the new one, set to new one
• otherwise, this is one of the periodic vertices: add a new vertex with the new coordinates, and use that in the element

We are using our legacy approach for now which duplicates all the vertices.

That is beside the point; we are looking for a way to detect periodicity early so we can set up metadata in VisIt properly.

[JustinPrivitera]

Do you know what T1 or P1 in the basis name refers to?

[pazner]

The algorithm that Tzanio describes sounds about right.

The meaning of the names is described here:

mfem/fem/fe_coll.hpp

Lines 128 to 129 in 17955e1

	| L2_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinuous L2 elements |
	| L2_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinuous L2 elements |

If the space has the form L2_dD_Pp, then the space is $d$ dimensional with degree $p$ polynomials.

If the space has the form L2_Tt_dD_Pp, then it additionally uses basis type t, where the basis types are defined here:

mfem/fem/fe/fe_base.hpp

Lines 28 to 42 in 17955e1

	enum
	{
	Invalid = -1,
	GaussLegendre = 0, ///< Open type
	GaussLobatto = 1, ///< Closed type
	Positive = 2, ///< Bernstein polynomials
	OpenUniform = 3, ///< Nodes: x_i = (i+1)/(n+1), i=0,...,n-1
	ClosedUniform = 4, ///< Nodes: x_i = i/(n-1), i=0,...,n-1
	OpenHalfUniform = 5, ///< Nodes: x_i = (i+1/2)/n, i=0,...,n-1
	Serendipity = 6, ///< Serendipity basis (squares / cubes)
	ClosedGL = 7, ///< Closed GaussLegendre
	IntegratedGLL = 8, ///< Integrated GLL indicator functions
	NumBasisTypes = 9 /**< Keep track of maximum types to prevent
	hard-coding */
	};

[JustinPrivitera]

Thank you, this is helpful. I think for now our approach will be to use the legacy refinement method for meshes with grid function bases that are L2.

[JustinPrivitera]

Your function mfem::Mesh::MakeRefined() cannot handle periodic meshes, so we use a legacy path. We want to know whether or not we can use mfem::Mesh::MakeRefined() down the line, and we want to know that when we are processing metadata.

[JustinPrivitera]

I think we've discussed this before with @tzanio and @v-dobrev. Are either of you aware of how to check if a mesh is periodic?