Re: Computer Limitations

[Kevin Thomas <kjt@sgi.com>]

To add to what Prof. Piket-May said, there is a way to estimate
the computational requirements of a model as well.  LC should really
incorporate some kind of "run time estimate", or possibly a
"time to completion estimate" (maybe both?), but currently you need
to do this calculation yourself.

First, get the problem size in megawords (not megabytes).  You can
have LC do this calculation for you (in the Run Simulation dialog),
or just divided the megabyte size by 4 (on an SGI computer) or by
8 (on a Cray).

There is approximately 1 floating point operation (FLOP) per word
of memory to complete a single time step.  Thus, a 4 megabyte simulation
requires 1 megawords of memory, and then 1 million FLOPs (1 megaflop)
per time step.  Since the boundary condition memory is automatically
included along with the main grid memory in the memory requirement
estimate, the boundary condition computation requirement is also
(roughly) approximated by this calculation.

Both Octane and Origin can be configured with many different MIPS
processors, so there's no single estimate of the computation speed,
but a good guess is in the 80 to 120 MFLOP range (lower if you have
195 MHz CPUs, higher if you have the new 300 MHz CPUs).
In our 1 megaflop simulation, each time step will take about 1/100th
of per CPU second, or 100 time steps per CPU second.  The wall clock
time (the time while you are waiting) might be longer than the CPU time
if the computer is being shared by lots of users, or if your model is
too large to fit in the computer's main memory.

Note that the far-field calculation doesn't fit this estimating method
very well if a large number of frequencies of interest is selected,
since the far-field calculation time will begin to dominate the run.
For bigger models with a single frequency of interest, the rough
calculation
is still pretty good.

For an estimate of the computation speed of your model on your computer,
look at the Run Simulation dialog display as a simulation is running.
A status message is displayed with the current computation speed.

In general, smaller models run at a faster MFLOP rate than larger ones
on SGI computers (due to the data cache and/or distributed memory).
The opposite is true of Cray (vector) computers, where smaller models
run at a lower MFLOP rate, while larger models run faster (due to
vector length).

For parallel processing, expect a near-linear or slightly super-linear
speedup for large models (25 megabytes per processor and larger).
So a 100 megabyte simulation should run twice as fast on two Origin
CPUs than on a single CPU.  Twice as fast means that the simulation
completes with half of the waiting time; of course the CPU time required
remains approximately constant.  There's no point to running with
multiple
CPUs on extremely small models; for example, the parallel speedup using
8 CPUs on a 1 megabyte simulation isn't going to be very impressive.

The main factor in the computation and memory requirements of LC is
the number of cells in the simulation grid, which is determined by the
model dimensions and the cell size.  So setting the cell size is
tricky, since it strongly affects the accuracy of the results.

There are two factors which should be considered when setting the cell
size: the minimum feature size of the model, and the frequency content
of the source excitation (or the frequencies of interest).  Minimum
feature size speaks for itself: you need the simulated model to closely
match the actual device, or else your results may be inaccurate.
Clever modelers often leave out details which they are certain won't
be significant for their simulations.  Even if you're not so well-versed
in electromagnetics, you can get a feel for how strongly your
simulations
are affected by physical features by running simulations with and
without
details that you'd like to omit, and see if there are big differences.

There is a rule of thumb for the other cell size factor, the source
excitation frequency; you should have at least 10 cells per wavelength
for the highest frequency of interest, and preferrably 20 or more.
A larger number of cells per wavelength is better, since then the
variation in electromagnetic field values can be better approximated
during the simulation.  The "View Source Waveforms" dialog in LC has
some graphical displays that can help determine if your source
excitation
has been properly resolved.  Remember that the wavelength is decreased
in materials with high relative permittivity (View Source Waveforms
takes
this crudely into account).

-- 
Kevin Thomas    kjt@cray.com   tel 1-651-683-3624
http://home.cray.com/~kjt/     or 1-800-284-2729 x33624