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Today's Topics:

   1.  nullspace within nonlinearvariationalsolver? (Sander Rhebergen)
   2. Re:  nullspace within nonlinearvariationalsolver?
      (Matthew Knepley)


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Message: 1
Date: Mon, 26 Aug 2019 21:37:11 +0000
From: Sander Rhebergen <srhebergen@uwaterloo.ca>
To: "firedrake@imperial.ac.uk" <firedrake@imperial.ac.uk>
Subject: [firedrake] nullspace within nonlinearvariationalsolver?
Message-ID: <d728cc7c78d84497a4a45da641289f9d@uwaterloo.ca>
Content-Type: text/plain; charset="iso-8859-1"

Hello,


Is it possible to set a constant nullspace for a NonlinearVariationalSolver?

I tried the following:


order = 2
V3 = FunctionSpace(mesh, "CG", order)
V1 = FunctionSpace(mesh, "BDM", order)
V2 = FunctionSpace(mesh, "DG", order-1)
W  = MixedFunctionSpace([V3, V1, V2])
v_basis = VectorSpaceBasis(constant=True)
null_space = MixedVectorSpaceBasis(W, [W.sub(0), W.sub(1), v_basis])


# Build Nonlinear Solver
uprob = NonlinearVariationalProblem(L, w1)
usolver = NonlinearVariationalSolver(uprob, nullspace=null_space, solver_parameters = {
    'snes_max_it': '50',
    'snes_rtol': '1e-12',
    'mat_type': 'aij',
    'ksp_type': 'preonly',
    'pc_type': 'lu',
    'snes_monitor': True,
    'snes_view': False,
    'snes_converged_reason': True,
    'ksp_converged_reason': True})

but the linear solver did not converge:


  0 SNES Function norm 7.964422825545e-02
  Linear firedrake_1_ solve did not converge due to DIVERGED_PCSETUP_FAILED iterations 0
                 PCSETUP_FAILED due to FACTOR_NUMERIC_ZEROPIVOT
Nonlinear firedrake_1_ solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0

I can send the full code if necessary. I'm trying to solve Navier-Stokes in velocity-vorticity-pressure formulation (https://arxiv.org/pdf/1604.00257.pdf) but the solver doesn't converge. If I add a small parameter times a pressure mass-matrix, the solver converges, but I was hoping to avoid doing this.


Thanks,

Sander


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Message: 2
Date: Mon, 26 Aug 2019 18:58:00 -0400
From: Matthew Knepley <knepley@gmail.com>
To: Sander Rhebergen <srhebergen@uwaterloo.ca>
Cc: "firedrake@imperial.ac.uk" <firedrake@imperial.ac.uk>
Subject: Re: [firedrake] nullspace within nonlinearvariationalsolver?
Message-ID:
        <CAMYG4Gm1rLmrZX8otNz+5YB8BpV6djXzsU2HPDUshAKjYHxNmQ@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"

On Mon, Aug 26, 2019 at 5:37 PM Sander Rhebergen <srhebergen@uwaterloo.ca>
wrote:

> Hello,
>
>
> Is it possible to set a constant nullspace for a
> NonlinearVariationalSolver?
>
> I tried the following:
>
>
> order = 2
> V3 = FunctionSpace(mesh, "CG", order)
> V1 = FunctionSpace(mesh, "BDM", order)
> V2 = FunctionSpace(mesh, "DG", order-1)
> W  = MixedFunctionSpace([V3, V1, V2])
> v_basis = VectorSpaceBasis(constant=True)
> null_space = MixedVectorSpaceBasis(W, [W.sub(0), W.sub(1), v_basis])
>
>
> # Build Nonlinear Solver
> uprob = NonlinearVariationalProblem(L, w1)
> usolver = NonlinearVariationalSolver(uprob, nullspace=null_space,
> solver_parameters = {
>     'snes_max_it': '50',
>     'snes_rtol': '1e-12',
>     'mat_type': 'aij',
>     'ksp_type': 'preonly',
>     'pc_type': 'lu',
>     'snes_monitor': True,
>     'snes_view': False,
>     'snes_converged_reason': True,
>     'ksp_converged_reason': True})
>
> but the linear solver did not converge:
>
>
>   0 SNES Function norm 7.964422825545e-02
>   Linear firedrake_1_ solve did not converge due to
> DIVERGED_PCSETUP_FAILED iterations 0
>                  PCSETUP_FAILED due to FACTOR_NUMERIC_ZEROPIVOT
> Nonlinear firedrake_1_ solve did not converge due to DIVERGED_LINEAR_SOLVE
> iterations 0
>

HI Sander,

Even if you set a nullspace here, you will get the same error because the
null space is not projected out, we just know
about it, thus LU will still fail. Getting the projected matrix would be
prohibitively expensive (I assume). Just to make sure,
the nullspace is constant pressure, right? I suggest either

  a) Using a Schur complement scheme, sticking the pressure mass matrix as
the PC matrix, and then using LU

or

  b) Using monolithic multigrid since you can use SVD on the coarse grid
with no problem

Or am I misunderstanding something. I have never used the VVP formulation.

 Thanks,

    Matt


> I can send the full code if necessary. I'm trying to solve Navier-Stokes
> in velocity-vorticity-pressure formulation (
> https://arxiv.org/pdf/1604.00257.pdf) but the solver doesn't converge. If
> I add a small parameter times a pressure mass-matrix, the solver converges,
> but I was hoping to avoid doing this.
>
>
> Thanks,
>
> Sander
>
>
>
> _______________________________________________
> firedrake mailing list
> firedrake@imperial.ac.uk
> https://mailman.ic.ac.uk/mailman/listinfo/firedrake
>


--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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End of firedrake Digest, Vol 32, Issue 9
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