[Beowulf] What class of PDEs/numerical schemes suitable for GPU clusters

[Mark Hahn]

> As we know by now GPUs can run some problems many times faster than CPUs

it's good to cultivate some skepticism.  the paper that quotes 40x
does so with a somewhat tilted comparison.  (I consider this comparison
fair: a host with 2x 3.2 GHz QC Core2 vs 1 current high-end CPU card.
former delivers 102.4 SP Gflops; latter is something like 1.2 Tflop.
those are all peak/theoretical.  the nature of the problem determines
how much slower real workloads are - I suggest that as not-suited-ness
increases, performance falls off _faster_ for the GPU.)

> what I understand GPUs are useful only with certain classes of numerical
> problems and discretization schemes, and of course the code must be

I think it's fair to say that GPUs are good for graphics-like loads,
or more generally: fairly small data, accessed data-parallel or with 
very regular and limited sharing, with high work-per-data.

> I'm part of a group that is purchasing our first beowulf cluster for a
> climate model and an estuary model using Chombo
> (http://seesar.lbl.gov/ANAG/chombo/). Getting up to speed (ha) on

offhand, I'd guess that adaptive grids will be substantially harder 
to run efficiently on a GPU than a uniform grid.

> than others? Given the very substantial speed improvements with GPUs,
> will there be a movement to GPU clusters, even if there is a substantial
> cost in problem reformulation?  Or are GPUs only suitable for a rather
> narrow range of numerical problems?

GP-GPU tools are currently immature, and IMO the hardware probably needs 
a generation of generalization before it becomes really widely used.
OTOH, GP-GPU has obviously drained much of the interest away from eg
FPGA computation.  I don't know whether there is still enough interest
in vector computers to drain anything...