On Thu, 19 Nov 2009, Jed Brown wrote:

> That could be tricky but you might be happy with just computing a
> low-bandwidth ordering and assembling into that, e.g.
> MatSetLocalToGlobalMapping, then insert with MatSetValuesLocal.  The
> ordering should cluster rows with identical sparsity pattern so you
> would benefit from inodes.

Block variable ordering with "--node_major_dofs" is perhaps the least
well-documented option in libMesh, which is saying a lot, but we're
already using it.

>> That's a shame, too.  One application I'm working on right now is
>> going to end up with roughly a half dozen variables on a big subdomain
>> and one or two dozen on a much bigger subdomain.  Storing block
>> structure alone would have been nice.
>
> Sounds like a lot of storage.

Well, the definition of "big" and "much bigger" is in the eye of the
beholder (and is going to depend on how much refinement we turn out to
need).  We're setting up a 128 core system for local testing; based on
some extrapolation and some results with a different code, I'm hoping
we'll be able to fit even the full problem on 64 cores without
exceeding per-node RAM.

> Are the blocks dense?

Not entirely, but close enough that we're not trying to shave a few
bytes on the exceptions, especially since it might just cost more
bytes in the sparsity pattern.

> Have you considered preconditioning with a sparser representation?

Barely, but we'll have to cross that bridge when we come to it.  For
the smaller problems we're using this code on now, there's still
memory to spare for ILU.  For later I'm not sure.  We'll have to
construct the true Jacobian for the adjoint problem, but might try to
set up a preconditioner based on reduced physics or a coarser grid.
---
Roy

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