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ParallelTable vs ParallelSubmit

Posted 10 years ago

I want to solve two ODEs in parallel which almost need the same time to solve. So I expected the parallel program to have approximately 50% of the running time of the serial one. This is true when I use ParallelSubmit but when I use ParallelTable the speedup is much lower.

Method          Walltime
Serial          3m10.647
ParallelSubmit  1m42.175s
ParallelTable   2m48.830s

Here are the codes I use:
ParallelSubmit

f := (
        d := 0.0000001;
        {time,tbl} = AbsoluteTiming[Table[{step, Timing[NDSolve[{x'[t] == x[t]^2 - x[t]^3, x[0] == d}, x, {t, 0, 2/d}, MaxStepSize->step, MaxSteps->10000000]]}, {step,5,5,-0.4}]];
)

g := (
        d := 0.0000001;
        {time,tbl} = AbsoluteTiming[Table[{step, Timing[NDSolve[{x'[t] == x[t]^2 - x[t]^3, x[0] == d}, x, {t, 0, 2/d}, MaxStepSize->step, MaxSteps->10000000]]}, {step,4.6,4.6,-0.4}]];
)

LaunchKernels[2];
DistributeDefinitions[f, g];
e = {ParallelSubmit[f], ParallelSubmit[g]};
WaitAll[e];

ParallelTable

d := 0.0000001;

LaunchKernels[2];
{time,tbl} = AbsoluteTiming[ParallelTable[{step, Timing[NDSolve[{x'[t] == x[t]^2 - x[t]^3, x[0] == d}, x, {t, 0, 2/d}, MaxStepSize->step, MaxSteps->10000000]]}, {step,5,4.6,-0.4}]];
CloseKernels[];

These diagrams show the CPU usage of both Methods:
ParallelSubmit
enter image description here
ParallelTable
enter image description here

ParallelSubmit looks as expected but ParallelTable looks like it uses different cores at different times. Especially at the end the picture is quite chaotic.

Is there a better way to use ParallelTable? Maybe an option I am missing?

POSTED BY: Matthias Neuer
4 Replies
POSTED BY: Chad Knutson

I think per ParallelTable's doc page it should distribute the definition automatically because DistributedContexts -> Automatic is preset. Omitting d should not affect the performance.

POSTED BY: Shenghui Yang
Posted 10 years ago

You are right there were some unnecessary lines in my codes. I deleted them but that didn't make any difference in the runtimes. I tried to distribute the definition of d but that made no difference either. I tested it with Mathematica 9.0 and 10.0.1. Which version did you use?

POSTED BY: Matthias Neuer

I looked at this more last week. I suspect that NDSolve rather than parallel tools is the source of the problem (your ode results in something quite close to a step function. Quite challenging to solve!). I tried several different implementations using ParallelSubmit, ParallelEvaluate, and ParallelTable. Computation time sometimes showed speedup and sometimes not. I also tried v9 and v10 and saw no significant differences between the two.

I will ask some people more familiar with NDSolve to take a look.

POSTED BY: Chad Knutson
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