Parallel solving and projecting using comm_world and comm_self

2

When you initialize a mesh with MPI.COMM_SELF you create a mesh (with all cells on each process).
This means that the mesh is not partitioned and you solve a problem for each mesh on each process.
If you use MPI.COMM_WORLD the mesh gets paritioned (one mesh distributed over multiple processes).

As to the execution time, I think you mean “why is solving solver than projecting?”.
Simply change your solve to solving inner(u, v)*dx instead of inner(grad(u), grad(v))*dx. What you will then realize, is that your solve function includes a projection (which is solving inner(u,v)*dx=inner(expr,v)).
If your change your solving function to:

def test_solving_time(mesh: fenics.Mesh):
    # define problem
    V = fenics.FunctionSpace(mesh, "CG", 1)
    expr = fenics.Expression("x[0] < 0.5 ? 1. : 0.", degree=1)
    u = fenics.TrialFunction(V)
    v = fenics.TestFunction(V)
    a = fenics.dot(u, v) * fenics.dx
    L = expr * v * fenics.dx
    u = fenics.Function(V)
    # solve
    fenics.solve(a == L, u, solver_parameters=solver_parameters)

you should get similar timings as projection.

If you use:

    a = fenics.dot(fenics.grad(u), fenics.grad(v)) * fenics.dx
    L = expr * v * fenics.dx
    u = fenics.Function(V)

in your solve function it will be marginally slower than projecting expr which has to do with the efficiency of the solver and preconditioner you are using (on a stiffness matrix and not a mass matrix).

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