[petsc-dev] Soliciting suggestions for linear solver work under SciDAC 4 Institutes

Mark Adams mfadams at lbl.gov
Fri Jul 8 07:16:10 CDT 2016

> The why is "We need to run at bandwidth peak on new arches". I do not
> prescribe the How, just ask for it.
Be careful about specifying an optimization parameter unless it is really
what you want.  eg, maximising arithmetic intensity will lead you
to Cayley–Hamilton inversion and minimizing ("avoiding") network
communication can lead to some funny algorithms if you are not careful.

Now, I suspect that maximizing bandwidth might not be gameable because that
is where Sam Williams ends up -- with large memory -- with HPGMG-FV, which
is matrix-free, 4th order accurate, finite volume, multigrid solver of the
3D Laplacian (non-constant coefficient). (While I hesitate to use one
person's experience as an implied "proof", Sam is very thorough and
honest.)  And keeping the memory bus saturated in the next 10 years may not
be achievable even for Sam.

But, in the space of equation solvers that are emerging architecture
friendly, you are latency constrained in practical -- not large memory --
regimes.  Though, large memory is a good place to start, a baseline, and
easier to think about and achieve. Still, I wince when I see a goal that
only implies good performance.
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