[petsc-users] Guidance on GAMG preconditioning

[Matthew Knepley]

On Thu, Jun 4, 2015 at 8:12 AM, Justin Chang <jychang48 at gmail.com> wrote:

> Hello everyone,
>
> Apologies if this sounds like a newbie question, but I am attempting to
> play around with the gamg preconditioner for my anisotropic diffusion
> problem, but I have no idea how to "fine tune" the parameters such that I
> get better performance. I understand that this depends on both the material
> properties and the type of mesh used, but I guess for starters, here is
> what I am doing and some stuff I have noticed:
>
> - I am solving a unit cube with a small hole in the middle. The outside BC
> conditions are 0 and the inside is unity. I have a tensorial dispersion
> diffusivity (with constant velocity). I have 6 different sized grids to
> solve this problem on. The problem sizes range from 36K dofs to 1M dofs. I
> was able to solve all of them using the CG and Jacobi solver and
> preconditioner combination.
>
> - When I try to solve them using CG and GAMG (I did not set any other
> command line options) I seem to get slower wall clock times but with much
> fewer KSP iterations. I also notice that the FLOPS/s metric is much smaller.
>
> - For certain meshes, my CG/GAMG solver fails to converge after 2
> iterations due to DIVERGED_INDEFINITE_PC. This does not happen when I solve
> this on one processor or with the CG/Jacobi solver.
>
> From what I have read online and through these petsc-mailing lists, it
> sounds to me the gamg preconditioner will give better performance for nice
> elliptic problems like the one I am solving. When I saw the SNES ex12 test
> case 39 from builder.py, it only had -pc_type gamg. I am guessing that I
> need to set additional command line options? If so, where should I start?
>

Mark recommends starting with

-ksp_type cg
-pc_type gamg
-pc_gamg_agg_nsmooths 1
-pc_gamg_threshold 0.02  #  [0 - 0.1]
#-mg_levels_ksp_type richardson
-mg_levels_ksp_type chebyshev
-mg_levels_pc_type sor
#-mg_levels_pc_type jacobi
-mg_levels_ksp_max_it 2   # [1-8]

and messing with the # stuff.

1) GAMG should definitely be more scalable than CG/ILU. You should be able
to see this by plotting the time/iterates as a function of problem size.
GAMG
    should have a constant number of iterates, whereas CG should grow. GAMG
will have higher overheads, so for smaller problem sizes CG can be better.

2)  The DIVERGED_INDEFINITE_PC can happen if the GAMG is non-symmetric due
to different number of iterates or the subsolver choice. Try out
     richardson instead of chebyshev.

3) If your coefficient is highly anisotropic, GAMG may need help making
good coarse basis vectors. Mark has some experimental stuff for this.
Adjusting the
    thresholding parameter determines how fast you coarsen (you can see the
coarse problem sizes in -ksp_view). If its too fast, convergence
deteriorates,
    too slow and the coarse problems are expensive.

    Mark, how do you turn on heavy-edge matching?

  Thanks,

     Matt


> Thanks,
> Justin
>



-- 
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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