Attribute multiple processes to independent solve (2-layer of parallelism)

Question

Hello there,

Consider the following code (fenics 2016.1), that allow to solve two probem in parallel, attributing a MPI communicator for each mesh:
(https://fenicsproject.org/qa/2682/solve-independent-equations-on-different-cores)

with mpirun -n 2 python program.py:

from dolfin import *
from mpi4py import MPI

# Communicator
mpi_comm = MPI.COMM_WORLD
# Rank 
rank_process = mpi_comm.rank

# Create mesh: one for each process
# create a mesh with a given MPI communicator is the key
if rank_process==0:
    mesh = UnitSquareMesh(mpi_comm_self(), 10, 10)
if rank_process==1:
    mesh = UnitSquareMesh(mpi_comm_self(), 20, 20)

# Plot mesh
plot_title= 'MESH for the process: {value}'.format(value=rank_process)
plot(mesh, title=plot_title, interactive=True)

# Function space and functions
V = FunctionSpace(mesh, "CG", 1)
u = TrialFunction(V)
v = TestFunction(V)
u_ = Function(V)

# Set source
if rank_process==0:
    source = Constant(1)
if rank_process==1: 
    source = Constant(-1)   

# Solve
solve(inner(grad(u), grad(v))*dx == source*v*dx, u_, bcs=DirichletBC(V, 0, "on_boundary"))

# Plot
plot(u_, title="Solution of the Proces {}".format(rank_process))
interactive()

Now, i would like that each problem (let's call them problem 1 and problem 2) use several process:

pseudo-code: of what i want to acheive:

mpirun - n NP python program.py

# Get number of DOF for each problem
DOF of probem 1
DOF of probem 2

# Attribute the number of process proportionally to the number of DOF
NP_for_problem1 = DOF of probem 1 / (DOF of probem 1 + DOF of probem 2) * NP 
NP_for_problem2 = DOF of probem 2 / (DOF of probem 1 + DOF of probem 2) * NP 

# Create mesh
# How to attribute multiple process to each mesh?
mesh_problem_1 = UnitSquareMesh(  ??? ,10, 10)  
mesh_problem_1 = UnitSquareMesh(  ??? , 20, 20)

etc. until solve

Comments

Do you need the solution for something else in your code? If not, have you tried setting the script to receive a parameter? You could use something like

mpirun -n 2 python main.py 1
mpirun -n 2 python main.py 2

and put that in a bash script (or windows or mac).

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That's another way to do indeed.
However, later in the code these two independent calculations are analyzed together. So, i would prefer to stick to one unique program if possible.
Any hints how to do it?

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No clue on how to do it in a single code. For it, I would export the solution in each code and then use another script for the analysis. Regards!

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Just a guess, but maybe the python multiprocessing module could help you, instead of using MPI (apparently no communication is needed between processes?).
See here: https://docs.python.org/3/library/multiprocessing.html