Dependencies questions

[Chris00]

The creation of a FiniteElementSpace takes a mutable pointer to a Mesh. I guess it is necessary to refine the mesh. However, it is not clear what happens to the FiniteElementSpace if the mesh is modified from the outside. It seems it is sufficient to call mfem::Mesh::NodesUpdated to update the Nodes (of type GridFunction) inside the space — but is it enough for the space? What if the space was used to create a LinearForm and/or a BilinearForm? Must these be considered invalid or is there a way to update them as well?

On a related topic, if the FiniteElementSpace is created from a mesh whose Nodes contains a FiniteElementCollection, must the FiniteElementCollection passed to the constructor be the same or may it be different (in which case, are there restrictions)?

Thanks!

CC: @mkovaxx

[tzanio]

On a related topic, if the FiniteElementSpace is created from a mesh whose Nodes contains a FiniteElementCollection, must the FiniteElementCollection passed to the constructor be the same or may it be different (in which case, are there restrictions)?

The short answer is that the spaces associated with the mesh and fields defined on it are generally different.

More specifically, if a mesh has Nodes defined, than the space for them represents the curvature of the elements, i.e. it tells us how we discretize the geometry of the problem. On any geometry, curved or not, we can define one or several finite element spaces for approximating PDE solutions, there are spaces don't need to be related to the space for the mesh. For example we can have 4th order H1 and 3rd orde L2 spaces on a linear mesh; or 0th L2 on a curved mesh; etc. That being said, there are fields like elasticity where the space for the displacements for which we solve a PDE is typically picked to be the same as the space for the mesh nodes.

Does this make sense?

[Chris00]

@tzanio Thank you for your very useful and quick answer.

I still am interested in the first part of my question. With @mkovaxx, we are trying to write a Rust binding for MFEM for which we must be careful to understand whether an argument may be mutated or not.

[tzanio]

Hi @Chris00, sorry for the delayed response.

The creation of a FiniteElementSpace takes a mutable pointer to a Mesh. I guess it is necessary to refine the mesh. However, it is not clear what happens to the FiniteElementSpace if the mesh is modified from the outside. It seems it is sufficient to call mfem::Mesh::NodesUpdated to update the Nodes (of type GridFunction) inside the space — but is it enough for the space? What if the space was used to create a LinearForm and/or a BilinearForm? Must these be considered invalid or is there a way to update them as well?

The space is defined on the provided mesh and more specifically on its topology. If the mesh Nodes are updated (and nothing else) the topology doesn't change and the space doesn't need to be updated. If the mesh is refined however, the space needs to be rebuild, which is what the Update() method is for. In that case any GridFunction, LinearForm and BilinearForm objects using the space need to be updated too, see e.g. Example 6.

Hope this helps,
Tzanio