On Wed, 12 Nov 2008, Vijay M wrote:

> Of course, I do not have any multi-grid support in my framework yet and so
> was wondering if there was a cleaner and elegant way to perform geometric
> multigrid. My main problem is that since mesh is associated with the
> EquationSystem, when I coarsen the mesh, all my systems are reinited and
> reallocated. And so it just seems too expensive to perform couple of cycles
> this way.

It definitely would be.  We wouldn't be averse to making library
changes to enable CPU-efficient geometric multigrid, but the amount of
work you'd have to do might not be programmer-efficient.

> In the meanwhile, if you have suggestions to perform geometric
> multigrid, do let me know.

I've never done it on any but toy code, so I'm not sure what the most
efficient way to do things would be.  For doing multiple multigrid
cycles per Newton step I think you'd want to store all the projection
& restriction operators and the coarse grid jacobians as sparse
matrices themselves to avoid having to do redundant FEM integrations.
But that sounds like it would roughly double your memory use.

And then there's the question of what to do with the Mesh and DoFMap.
We'd finally use the "subactive" element capabilities to provide
different active level views of the same mesh, but DoF indexing
(especially with non-Lagrange elements!) would be tricky; we'd need
to keep track of per-level global dof indices, not just the (maximum
of) 2 that we use now.
---
Roy

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