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