[petsc-dev] Non-scalable matrix operations

[Mark F. Adams]

On Dec 23, 2011, at 12:02 PM, Jed Brown wrote:

> On Fri, Dec 23, 2011 at 10:48, Mark F. Adams <mark.adams at columbia.edu> wrote:
> There is the implementation in Prometheus that uses my C++ linked lists and hash tables.  I would like to implement this with STLs.  I also hack into MPIAIJ matrices to provide a primitive of applying G-S on an index set of local vertices, required for the algorithm.  This should be rethought.  I would guess that it would take about a week or two to move this into PETSc.
> 
> The complex communication required make this code work much better with large subdomains, so it is getting less attractive in a flat MPI mode, as it is currently written.  If I do this I would like to think about doing it in the next programming model of PETSc (pthreads?).  Anyway, this would take enough work that I'd like to think a bit about its design and even the algorithm in a non flat MPI model.
> 
> Note, I see the win with G-S over Cheby in highly unsymmetric (convection, hyperbolic) problems where Cheby is not very good.
> 
> Can we mix with Eisenstat to apply multiple cycles?

Eisenstat is not computing with zero data if there is no initial guess, right?  I'm not sure I understand you here.

> I know the theory doesn't argue for it, but G-S with Cheby sometimes wins over everything else I've tried.

People damp G-S for convection etc, which is what Cheb/GS does.  Do you do this for SPD systems?

> Is there any hope of doing nonlinear G-S where the user can provide something moderately simple?

Nonlinear should be very simple actually.  Just replace my hacks into (MPI)AIJ matrices with your own operator.

Mark
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