I am trying to do some Numerical Integration in parallel using ParallelSubmit and WaitAll. The code is this,
WaitAll[{
ParallelSubmit[NIntegrate[Integrand1Test[0.4,thA,phiA,0.5,thC,phiC,0,0,0]
Sin[thA] Sin[thC],{phiC,0,2 \[Pi]},{phiA,0,2 \[Pi]},{thA,0,\[Pi]},{thC,0,\[Pi]}]],
ParallelSubmit[NIntegrate[Integrand2Test[.4,thA,phiA,.5,thC,phiC,0,0,0]
Sin[thA]Sin[thC],{phiC,0,2\[Pi]},{phiA,0,2\[Pi]},{thA,0,\[Pi]},{thC,0,\[Pi]}]],
ParallelSubmit[NIntegrate[Integrand3Test[.4,thA,phiA,.5,thC,phiC,0,0,0]
Sin[thA]Sin[thC],{phiC,0,2\[Pi]},{phiA,0,2\[Pi]},{thA,0,\[Pi]},{thC,0,\[Pi]}]],
ParallelSubmit[NIntegrate[(Integrand4Test[.4,thA,phiA,.5,thC,phiC,0,0,0]-Integrand5Test[.4,thA,phiA,.5,thC,phiC,0,0,0])
Sin[thA]Sin[thC],{phiC,0,2\[Pi]},{phiA,0,2\[Pi]},{thA,0,\[Pi]},{thC,0,\[Pi]}]],
ParallelSubmit[NIntegrate[Integrand6Test[.4,thA,phiA,.5,thC,phiC,0,0,0]
Sin[thA]Sin[thC],{phiC,0,2\[Pi]}, {phiA,0,2\[Pi]},{thA,0,\[Pi]},{thC,0,\[Pi]}]]}]//AbsoluteTiming
These integrations are independent of each other. The output is this: (besides some warnings from the numerical integration)
{288.921,{RefLink[ParallelSubmit,paclet:ref/ParallelSubmit][-0.00279665],
RefLink[ParallelSubmit,paclet:ref/ParallelSubmit][0.342983],
RefLink[ParallelSubmit,paclet:ref/ParallelSubmit]-0.559774],
RefLink[ParallelSubmit,paclet:ref/ParallelSubmit][-0.0569992+0. I],
RefLink[ParallelSubmit,paclet:ref/ParallelSubmit][-0.0309274+0. I]}}
I don't know what does "RefLink[ParallelSubmit,paclet:ref/ParallelSubmit]" mean? The examples in mathematica documents and tutorials run OK without these messages. The numbers in the "[ ]" are the integration result.
The other problem is that I use top and htop (on linux) to look at the CPU usage, and see that only one CPU core is working 100%, the others are only less than %5. This means that it run only on one CPU core. There is also one similar problem I googled in here https://mathematica.stackexchange.com/questions/132366/parallelsubmit-executes-only-on-one-kernel .
The Parallelize command seems to do well. Is the ParallelSubmit & WaitAll combination buggy?