Re: parallel computing toolkit
- To: mathgroup at smc.vnet.net
- Subject: [mg24076] Re: parallel computing toolkit
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 23 Jun 2000 02:26:43 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <8is6ln$h0e@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
parallel Runge-Kutta Method for two processors
(the ratio can't be better than 2) for
a n-Dimensional system, the system was sparse
but the implicit solver make a full LUSolution
{y[1]'[t] == y[1][t]*(y[2][t] - y[n][t]),
Sequence @@
Table[y[i]'[t] == y[i][t]*(y[i + 1][t] - y[i - 1][t]), {i, 2, n -
1}],
y[n]'[t] == y[n][t]*(y[1][t] - y[n -
1][t]), y[1][0] ==
1
Sequence @@ Table[y[i][0] == 1/8, {i, 2,
n}]}
Mathematica && parallel computing toolkit
Dimension Serial Parallel
of the eqns [s] [s]
4, 4. 29.
8, 5. 4.
16, 10. 6.
32, 28. 15.
64, 94. 48.
128, 326. 162.
256, 1410. 703.
1024, 15332. 7684.
Same algorithm with a seriel/parallel
MathLink program
4, 0.3 1.34,
8, 0.39 1.39,
16, 0.79 1.51,
32, 2.1 2.25,
64, 6.07 4.96,
128, 20.73 13.27,
256, 97.6 53.22,
512, 740.06 414.99
All experiments on a Dual UltraSparc 200 MHz
So, if you make stupid numerics you should
not use the parallel computing tool kit.
If you have a symbolic algorithm that
need Mathematica than it is easy to
get a speed gain when you can live with the
master/worker model. Make an other topologie
seems to be hard. I had tryed a chain topologie
but I was not able to synchronize the transfer
between the chain member without the help of the
master.
Hope that helps
Jens
Nicolas Regnault wrote:
>
> Hi,
>
> I'm interested in finding benchmarks for Mathematica with the new parallel
> computing toolkit (especially for biprocessor PC). Does anybody know where I
> could find such informations (or perhaps someone could tell me his own
> experience).
>
> Thanks