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MathGroup Archive 2000

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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


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