Make MeshHierarchy implicit?

[connorjward]

Currently when we want to use multigrid we have to first create a MeshHierarchy object. I think it's possible that we could now hide this extra implementation step and users could just create forms directly on the initial mesh they create.

I think that this is now possible because we have changed mesh initialisation substantially, and in particular have eliminated the requirement that a mesh hierarchy be constructed before function spaces are made.

[pbrubeck]

Would you like an MG interface through NonlinearVariationalSolver? The user still needs to prescribe the number of refinements somehow. And should the solver now return the solution (which they would not have access if they had not created the fine mesh).

Or would you propose mesh = UtilityMesh(..., uniform_refinements=3) instead of

base = UtilityMesh(...)
mh = MeshHierarchy(base, 3)
mesh = mh[-1]

[pbrubeck]

Take a look at what we have done for GoalAdaptiveVariationalSolver in #4893. There the adaptive hierarchy is built on the fly, by estimating the error after solving the problem on each level.

[connorjward]

Would you like an MG interface through NonlinearVariationalSolver? The user still needs to prescribe the number of refinements somehow. And should the solver now return the solution (which they would not have access if they had not created the fine mesh).

Good points. I confess I hadn't really thought through any specifics here. It would be easier to do coarsening behind the scenes instead of refinement. But that's suddenly a lot of work.

I just wanted to point out that we suddenly have more flexibility regarding the interface than we did before.

[pbrubeck]

Coarsening is very hard in general

[connorjward]

Maybe this "enhancement" suggestion should be closed then. I didn't appreciate initially how important it is that the user handle both the coarsest and finest mesh.