Many thanks, Wolfgang. Yes, I need to solve for the basis in each coarse
cell separately, i.e., I have as many local fine meshes as coarse cells.
I think that's actually an important point you are making here, maybe
inadvertently: You have as many *meshes* as there are coarse cells.
Now, just refining the global mesh a number of more times gives you
another global mesh, but it does not give you a mesh for each coarse cell.
In my deal.II classes, I've had students solve problems like yours and
they typically just build one new triangulation for each coarse mesh
cell, then attach a DoFHandler to it, and solve problems on them. That
is likely not very efficient if you want to solve real problems, but
it's good enough for small testcases and it allows for easy
parallelization using threads.
On the other hand, if you were to build a global DoFHandler on the
refined mesh, you'd have to define what to do with those DoFs that lie
outside the patch (that results from a single coarse mesh) you are
currently considering. You'd likely want to set these to zero, but
they're still there, and the resulting patch problem will be large. It's
also much more difficult to do things in parallel because now you have
one global (fine) mesh that you want to use for multiple things at the
same time.
Do you think it would be possible to (ab)use the multigrid classes for
that? As far as I understand there are dofhandlers on each level of the
mesh. Can I get dofhandlers for all active subcells of say coarse cell
number n in level 5?
No. The multigrid DoFHandler functionality considers each level as a
whole. You can't pick and choose.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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