[Beowulf] Why one might want a bunch o' processors under your desk.

[Jim Lux]

Today I was running a lot of antenna models, using a method of moments code 
called NEC4 (in FORTRAN).
Just to describe the computational task for context:

The antenna I am modeling is 9 patches, in a square grid, the middle one of 
which is excited.

Basically, it breaks the antenna into a whole bunch of segments (1981 of 
them in my model), calculates the interactions between them (i.e. if you 
have a voltage in segment i, what current does that induce in segment j) 
making a square matrix some 2000x2000.  It then solves for the currents 
given an excitation, giving you a vector of some 1981 currents.  The sum of 
the radiated fields is calculated at points covering a hemisphere (8326 of 
them in my case).

The process is, as one might imagine, highly compute intensive (i.e. 
there's not much disk access going on, after the 10 line file describing 
the geometry has been read in).  The matrix math routines have been (I've 
been told) highly optimized for the Pentium architecture.

On a P4 1.7GHz, it uses 64MB of RAM, and takes about 21 seconds to fill the 
matrix (that's the calculating the interactions part), and about 49 seconds 
to calculate the currents.  Calculating the actual far field pattern takes 
about 126 seconds. (Interestingly, I ran it on my new HP Tablet too, which 
has a Pentium M 1GHz(nom) processor.. the first two steps were about the 
same speed (slightly faster), but the last was much slower, and the fan was 
merrily spinning... I suspect it slowed down because it got too hot (speed 
reported as 590 MHz, not 1000 MHz)

OK.. both of these are Windows (2000 or XP), but run times on comparable 
Linux systems are about the same (not much OS activity going on in either 
case).

In any case, this is a long enough run time (3.5 minutes) that it's not 
interactive.  It's definitely a "start it and go get coffee down the hall" 
time span.

This is for one frequency.  Now, say I wanted to run the model for, say, 
100 different frequencies (which I do).  We're looking at 350 minutes, or 
the better part of a day.

Or, more importantly, I want to assess the effects of small changes in the 
orientation and position of the elements (what are my construction 
tolerances?). Maybe a Monte Carlo analysis, changing parameters using some 
random numbers.  Can I arrange them differently and get more tolerance?

In any case, this is a problem ripe for parallelizing. One could 
parallelize the pattern computation (i.e. calculate the matrix once and 
split the 8000 points among multiple processors).  Or, for the parametric 
studies, calculate different frequencies (which requires redoing the 
matrix, since everything is wavelength dependent) on different processors.

It's a design problem ripe for interaction too.  There's a lot of 
parameters I can change (size and shape of the patches, segmentation, 
spacing, etc.), so running a "try all possible values of all variables 
overnight" strategy won't work.  Equally poor would be a "submit massive 
batch job to the JPL DELL 1024 processor cluster", mostly because the 
design space probably spans several thousand parameter combinations.  I 
want to try a few things, then try some more, and use my experience to 
guide the process, not depend on a optimizing program, for which I'd have 
to come up with a goal function that is sort of ill-defined.

Oh yeah, what I REALLY want to do is simulate an antenna with several 
hundred patches, not just 9.

What I DON'T want to do is rewrite (or even recompile) the antenna modeling 
code. It works, it's been validated, it's been optimized (to a certain 
extent), and besides, my job is to use the code, not to rewrite it for 
parallel computing.

And yes, there are approximations, better modeling codes, etc. 
available.  But again, I'd like to avoid having to track them down, 
validate them, and so forth. I want to run my tried and true (but slow) 
code, faster.

I suspect that I am not alone.  There are probably hundreds of people who 
have similar kinds of problems, and would be well served by a desktop or 
personal supercomputer.

Flame On!!




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