Parallel computing NInverseFourierTransForm

Question

I am running the code below, and it works perfectly. I have some function in Fourier space, and I take the numerical InverseFourierTransform. However, I will have to repeat this calculation often, and therefore I want to use ParallelTable. I've tried this, by replacing Table in the code below by ParallelTable. I am running the code on a computer with 8 kernels. Surprisingly, using ParallelTable doesn't speed up the calculation. I simply find almost the same computation time (not roughly a factor 8 difference)!

Can anybody explain to me what the reason for this is? I've tested the ParallelTable with commands like

  ParallelTable[Pause[1]; f[i], {i, 4}] // AbsoluteTiming

and for this case it works fine, but not for the NInverseFourierTransform.

ClearAll["Global`*"];
f[q_] := Sqrt[2/Pi]*(-Sinc[q] + Cos[q]);
k[q_] := Sqrt[Pi/2]/Abs[q];
a = 10^-2;
b = 10^-2;
Needs["FourierSeries`"]
hfourierdomain[ω_] = a*f[ω]*k[ω]/(1 + b*ω^2*k[ω]);
displ = Table[{j, NInverseFourierTransform[hfourierdomain[ω], ω, j]}, {j, -5, 5, 1/60}];

Answer 1

When I run your code on my machine with Table (not ParallelTable), I see that all the cores of the CPU are used by a single MathKernel process. This means that internally NInverseFourierTransform uses an operation that is already parallelized. Certain operations, such as LinearSolve, will be able to use all cores of your CPU even when run on a single kernel.

Because of this the Table version is likely already as efficient as it can be, and splitting the task into several parts and distributing it among kernels (which will individually all want to use all your CPU cores) is likely to just reduce performance.

P.S. If your CPU has 4 cores and supports hyperthreading (e.g. many i7 processors), your OS will show 8 cores in total out of which 4 are working.