[petsc-users] Starting point for Stokes fieldsplit

[Dave May]

Hey Max,

Without knowing anything about the specific application related to
your Stokes problem, or information about the mesh you are using, I
have a couple of questions and suggestions which might help.

1) If  A, is your stokes operator A = ( K,B ; B^T, 0 ), what is your
precondition operator?
Specifically, what is in the (2,2) slot in the precondioner? - i.e.
what matrix are you you applying -stokes_fieldsplit_1_pc_type jacobi
-stokes_fieldsplit_1_ksp_type preonly to?
Is it the identity as in the SpeedUp notes?

2) This choice
-stokes_fieldsplit_0_pc_type ml -stokes_fieldsplit_0_ksp_type preonly
may simply not be a very effective and degrade the performance of the
outer solver.
I'd make the solver for the operator in the (1,1) slot much stronger,
for example
  -stokes_fieldsplit_0_ksp_type gmres
  -stokes_fieldsplit_0_ksp_rtol 1.0e-4
  -stokes_fieldsplit_0_mg_levels_ksp_type gmres
  -stokes_fieldsplit_0_mg_levels_pc_type bjacobi
  -stokes_fieldsplit_0_mg_levels_ksp_max_it 4

Add a monitor on this solver (-stokes_fieldsplit_0_ksp_XXX) to see how
ML is doing.

3) Using -stokes_pc_fieldsplit_type MULTIPLICATIVE should reduce the
number of outer iterations by a factor of two, but it will use more
memory.

4) You should use a flexible Krylov method on the outer most solve
(-stokes_ksp_XXX) as the preconditioner is varying between each outer
iteration. Use -stokes_ksp_type fgmres or -stokes_ksp_type gcr

5) Depending on how the physical problem is scaled
(non-dimensionalised), the size of the residuals associated with the
momentum and continuity equation make be quite different. You are
currently use the entire residual from (u,p) to determine when to stop
iterating. You might want to consider writing a monitor which examines
the these residuals independently.


Cheers,
  Dave


On 20 February 2012 08:04, Max Rudolph <rudolph at berkeley.edu> wrote:
> I am solving a 2D Stokes flow problem using a finite volume discretization, velocity (dof 0,1)-pressure (dof 2) formulation. Until now I have mostly used MUMPS. I am trying to use the PCFieldSplit interface now, with the goal of trying out the multigrid functionality provided through ML. I looked at these (http://www.mcs.anl.gov/petsc/documentation/tutorials/Speedup10.pdf) talk slides for some guidance on command line options and tried. When assembling the linear system, I obtain the global degree-of-freedom indices using DMDAGetGlobalIndices. The solver does not appear to be converging and I was wondering if someone could explain to me why this might be happening. Thanks for your help.
>
> Max
>
> petscmpiexec -n $1 $2 $3 \
> -stokes_pc_fieldsplit_0_fields 0,1 -stokes_pc_fieldsplit_1_fields 2 \
> -stokes_pc_type fieldsplit -stokes_pc_fieldsplit_type additive \
> -stokes_fieldsplit_0_pc_type ml -stokes_fieldsplit_0_ksp_type preonly \
> -stokes_fieldsplit_1_pc_type jacobi -stokes_fieldsplit_1_ksp_type preonly \
> -stokes_ksp_view \
> -stokes_ksp_monitor_true_residual \
>
>  Residual norms for stokes_ solve.
>  0 KSP preconditioned resid norm 2.156200561011e-07 true resid norm 1.165111661413e+06 ||r(i)||/||b|| 1.000000000000e+00
>  1 KSP preconditioned resid norm 2.156200561011e-07 true resid norm 1.165111661413e+06 ||r(i)||/||b|| 1.000000000000e+00
>  2 KSP preconditioned resid norm 5.176186579848e-08 true resid norm 5.747484453195e+06 ||r(i)||/||b|| 4.932990239085e+00
>  3 KSP preconditioned resid norm 5.054067588022e-08 true resid norm 5.763708451168e+06 ||r(i)||/||b|| 4.946915082953e+00
>  4 KSP preconditioned resid norm 3.556841873413e-08 true resid norm 4.649778784249e+06 ||r(i)||/||b|| 3.990843915003e+00
>  5 KSP preconditioned resid norm 3.177972840516e-08 true resid norm 4.677248322326e+06 ||r(i)||/||b|| 4.014420657890e+00
>  6 KSP preconditioned resid norm 3.100188857346e-08 true resid norm 4.857618195959e+06 ||r(i)||/||b|| 4.169229745814e+00
>  7 KSP preconditioned resid norm 3.045495907075e-08 true resid norm 5.030091724356e+06 ||r(i)||/||b|| 4.317261504580e+00
>  8 KSP preconditioned resid norm 2.993896937859e-08 true resid norm 5.213745290794e+06 ||r(i)||/||b|| 4.474888942808e+00
>  9 KSP preconditioned resid norm 2.944838631679e-08 true resid norm 5.403745734510e+06 ||r(i)||/||b|| 4.637963822245e+00
>  10 KSP preconditioned resid norm 2.898115557667e-08 true resid norm 5.596205405394e+06 ||r(i)||/||b|| 4.803149423985e+00
>  11 KSP preconditioned resid norm 2.853548106431e-08 true resid norm 5.788329048801e+06 ||r(i)||/||b|| 4.968046617765e+00
>  12 KSP preconditioned resid norm 2.810975464206e-08 true resid norm 5.978285004145e+06 ||r(i)||/||b|| 5.131083313418e+00
>  13 KSP preconditioned resid norm 2.770253127208e-08 true resid norm 6.164551408716e+06 ||r(i)||/||b|| 5.290953316217e+00
>  14 KSP preconditioned resid norm 2.731250834421e-08 true resid norm 6.346469882864e+06 ||r(i)||/||b|| 5.447091547575e+00
>  15 KSP preconditioned resid norm 2.693850812065e-08 true resid norm 6.523343466838e+06 ||r(i)||/||b|| 5.598899816114e+00
>