[petsc-users] How to improve this solver for Navier-Stokes equation (based on fieldsplit and lsc)

[Matthew Knepley]

On Thu, Jun 14, 2012 at 10:07 PM, Thomas Witkowski <
thomas.witkowski at tu-dresden.de> wrote:

>  Am 14.06.2012 15:06, schrieb Matthew Knepley:
>
> On Thu, Jun 14, 2012 at 9:01 PM, Thomas Witkowski <
> thomas.witkowski at tu-dresden.de> wrote:
>
>> I try to implement an efficient solver for my FEM based unsteady Navier
>> Stokes code. The scenario I consider is realy simple: 2D FEM with
>> Taylor-Hood element, equi-spaced grid, simple channel flow with prescribed
>> inflow boundaries for the velocity, no boundary conditions for the
>> pressure. Because I want to
>
>
>  With no pressure BC, you need to specify the null space. Look at SNES
> ex62.
>
> As so often, I forgotten about this :) As I have free outflow boundary for
> the velocity (so no Dirichlet boundary), I think, the nullspace must be
> somehow different than just setting a constant on all pressure nodes. So I
> want back to the even more simple case, the driven cavity scenario. Here I
> have dirichlet BC on all velocity components and boundaries and no pressure
> BC. There is no influence on the solver, whether I set the null space or
> not (I checked for it with -ksp_view that there is a null space set). Only
> when going from fgmres to gmres for the outer solver, setting the null
> space has some (positive) change in the solver convergence.
>

It has a null space, so whatever you observe in a single run is an outlier.
Try removing the null space in ex62. It will fail to converge.


>
>
> solve unsteady flows, at each timepoint an Ossen problem is solved
>> (implicit Euler time discretization, "trivial" linearization). For using
>> PETSc, I created a fieldsplit preconditioner, that is configured in the
>> following way:
>>
>> mpirun -np 2 ./navier_stokes init/channel_parallel.dat.2d \
>> -ksp_type fgmres \
>> -pc_type fieldsplit \
>> -pc_fieldsplit_type SCHUR \
>> -pc_fieldsplit_schur_fact_type FULL \
>> -ksp_converged_reason \
>> -ksp_monitor_true_residual \
>> -fieldsplit_velocity_ksp_type preonly \
>> -fieldsplit_velocity_pc_type lu \
>> -fieldsplit_velocity_pc_factor_mat_solver_package mumps \
>> -fieldsplit_pressure_ksp_type gmres \
>> -fieldsplit_pressure_ksp_max_it 10 \
>> -fieldsplit_pressure_ksp_rtol 1.0e-2 \
>> -fieldsplit_pressure_pc_type lsc \
>>
>
>  This makes no sense unless you specify an auxiliary operator. Just leave
> it at jacobi. When you use LU
> for velocity, it will converge in 1 iterate. Since it doesn't, it means
> you have a problem with the null space.
>
> So even for the driven cavity, the null space is set, and again I use the
> same solver, it needs something like 10 or 15 iterations. I don't
> understand your argument, that using LU for the velocity part, this solver
> should converge in 1 iterations. It still has an inexact solver for the
> Schur complement and the solver for the composite matrix in LSC is also
> inexact.
>

1) Start with -fieldsplit_pressure_ksp_rtol 1e-10. It will converge in 1
iterate. Back off the Schur tolerance
    to balance that cost with the cost of extra iterates. This is the game.

2) Again, LSC is not doing anything for you right now, unless you are
indeed giving an auxiliary operator. Use jacobi.

   Matt


> Thomas
>
>
>     Matt
>
>
>> -fieldsplit_pressure_lsc_ksp_type bcgs \
>> -fieldsplit_pressure_lsc_ksp_max_it 10 \
>> -fieldsplit_pressure_lsc_ksp_rtol 1.0e-2 \
>> -fieldsplit_pressure_lsc_pc_type hypre
>>
>> The direct solver for the velocity part is just for debugging and should
>> be replaced when everything else works fine. The point is, that I found
>> this constellation to be not very efficient. It takes around 20 to 30
>> iterations, which takes around 30 seconds on a very small problem size
>> (around 20000 global unknows for each velocity component and 5000 global
>> unknowns for the pressure) on a very fast desktop CPU (some new Intel Xeno
>> with 4 core). Any hints for improvements?
>>
>> Thomas
>>
>
>
>
>  --
> 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
>
>
>


-- 
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
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