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

[Finch, Ralph]

As we know by now GPUs can run some problems many times faster than CPUs
(e.g. http://folding.stanford.edu/English/FAQ-highperformance). From
what I understand GPUs are useful only with certain classes of numerical
problems and discretization schemes, and of course the code must be
rewritten to take advantage of the GPU.

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
clusters I started wondering if packages like Chombo, and numerical
problems generally, would be rewritten to take advantage of GPUs and GPU
clusters, if the latter exist.  From decades ago when I actually knew
something I vaguely recall that PDEs can be classed as to parabolic,
hyperbolic or elliptic. And there are explicit and implicit methods in
time.  Are some of these classifications much better suited for GPUs
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?

Ralph Finch, P.E.
California Dept. of Water Resources
Delta Modeling Section, Bay-Delta Office
Room 215-13
1416 9th Street
Sacramento CA  95814
916-653-7552
rfinch at water.ca.gov