[petsc-dev] New implementation of PtAP based on all-at-once algorithm

[Mark Adams]

>
> So you could reorder your equations and see a block diagonal matrix with
>> 576 blocks. right?
>>
>
> I not sure I understand the question correctly. For each mesh vertex, we
> have a 576x576 diagonal matrix.   The unknowns are ordered in this way:
> v0, v2.., v575 for vertex 1, and another 576 variables for mesh vertex 2,
> and so on.
>

My question is,mathematically, or algebraically, is this preconditioner
equivalent to 576 Laplacian PCs? I see that it is not because you coarsen
the number of variables per node. So your interpolation operators couple
your equations. I think that other than the coupling from eigen estimates
and Krylov methods, and the coupling from your variable coursening that you
have independent scalar Laplacian PCs.

10 levels is a lot. I am guessing you do like 5 levels of variable
coarsening and 5 levels of (normal) vertex coarsening with some sort of AMG
method.

This is a very different regime that problems that I am used to.

And it would still be interesting to see the flop counters to get a sense
of the underlying performance differences between the normal and the
all-at-once PtAp.
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