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

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