more on structural models for clusters

[Jim Lux]

At 05:29 PM 10/2/2003 -0700, Bill Broadley wrote:
>On Wed, Oct 01, 2003 at 03:36:35PM -0700, Jim Lux wrote:
> > In regards to my recent post looking for cluster implementations for
> > structural dynamic models, I would like to add that I'm interested in
> > "highly distributed" solutions where the computational load for each
> > processor is very, very low, as opposed to fairly conventional (and widely
> > available) schemes for replacing the Cray with a N-node cluster.
> >
> > The number of processors would be comparable to the number of structural
> > nodes (to a first order of magnitude)
>
>Er, why bother?  Is there some reason to distribute those things so
>thinly?  Your average dell can do 1-4 Billion floating point ops/sec,
>why bother with so few per CPU?  Am I missing something?


Your average Dell isn't suited to inclusion as a MCU core in an ASIC at 
each node and would cost more than $10/node...  I'm looking at Z80/6502/low 
end DSP kinds of computational capability in a mesh containing, say, 
100,000 nodes.

Sure, we'd do algorithm development on a bigger machine, but in the end 
game, you're looking at zillions of fairly stupid nodes.  The commodity 
cluster aspect would only be in the development stages, and because it's 
much more likely that someone has solved the problem for a Beowulf (which 
is fairly loosely coupled and coarse grained) than for a big multiprocessor 
with tight coupling like a Cray.

Haven't fully defined the required performance yet, but, as a starting 
point, I'd need to "solve the system" in something like 100 
microseconds.  The key is that I need an algorithm for which the workload 
scales roughly linearly as a function of the number of nodes, because the 
computational power available also scales as the number of loads.

Clearly, I'm not going to do a brute force inversion or LU decomposition of 
a 100,000x100,000 matrix...  However, inverting 100,000 matrices, each, 
say, 10x10, is reasonable.

 >Bill Broadley
 >Mathematics
 >UC Davis

James Lux, P.E.
Spacecraft Telecommunications Section
Jet Propulsion Laboratory, Mail Stop 161-213
4800 Oak Grove Drive
Pasadena CA 91109
tel: (818)354-2075
fax: (818)393-6875

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