Partitioning of 3D mesh connected along edge

[Jari]

I have a somewhat degenerated mesh consisting of two regions which are connected just along an edge. The mesh was originately created in dolfinx v.0.5.0 via create_box(..., GhostMode.shared_facet) and later individual elements were removed using meshio. The image below illustrates a simple linear elasticity problem. It works perfectly fine in serial, but connectivity is lost if run in parallel. The blue and red colors indicate the partitioning for two processes.

Although parallelization is not crucial in my particular application, I might be curious whether there is a way to fix this?

[dokken]

Having a mesh connected by a mesh is not recommended for elasticity, as it produces singularities. It is also not supported in parallel in DOLFINx, as the partitioning goes through shared_facets.

See for instance Defining non-CG1 FunctionSpace in parallel on mesh resulting from local mesh refinement - #2 by dokken
for a general mesh checker.