[petsc-users] unreliable AMG in PETSc

[Arne Morten Kvarving]

On 22/10/14 23:17, Barry Smith wrote:

hi barry,

thanks for your fast response.

>    Arnem,
>
>     I was able to reproduce your failures. ml is a rather old code from Sandia that is not getting new development (they are working on a complete replacement for several years).
>
>     I ran you tests using the PETSc AMG solver -pc_type gamg (written largely by Mark Adams) using its default options and it converged for all your cases from 1 to 32 processes with no failure of positive definiteness etc.
i can confirm it works fine with the default options. however, i can 
easily fault gamg as well - turn on richardson ksps and poof.

27 - amg_14 (Failed)
39 - amg_20 (Failed)
41 - amg_21 (Failed)
43 - amg_22 (Failed)
45 - amg_23 (Failed)
49 - amg_25 (Failed)
51 - amg_26 (Failed)
53 - amg_27 (Failed)
55 - amg_28 (Failed)
57 - amg_29 (Failed)
61 - amg_31 (Failed)
63 - amg_32 (Failed)

seems the use of chebyshev is a part of the cure, not just the 
agglomerator. in particular if i run ml with chebyshev the failures are 
reduced to

43 - amg_22 (Failed)
45 - amg_23 (Failed)
53 - amg_27 (Failed)
61 - amg_31 (Failed)
63 - amg_32 (Failed)

unless my memory fails me, chebyshev is used to ensure the linear 
dependency of the preconditioner on the residual. in particular it's a 
suitable iterative solver for the coarse solve.

so i think the fact that it cures things indicates that something breaks 
the linear property.

hopefully the eigenvalue estimates aren't too expensive and i can run 
this setup on the real deal. will play.

>
>     That said the convergence rate is not super-great, around 70+ iterations and I did not run for timing comparisons. But
>
> 75 iterations on 1 processors
> 76 iterations on 16 processors
> 78 iterations on 32 processors
yes, as i said do not pay much attention to this. the real code uses 
line / plane smoothers due to the large cell aspect ratios of the mesh 
(10^3-10^4). when it works it uses ~ 15 iterations.

>    Do not run it with PETSc 3.4, only with PETSc 3.5
i played with gamg a year or so ago and concluded that it was a 
crashfest, divergencefest etc.
i interpret your reponse here to mean that it has gotten quite some 
attention lately?
>
>    I would suggest you run with gamg and send us reports on problems that come up and drop ml. We are actively interested in improving gamg based on your feedback.
good stuff. you have my first report above :)

cheers

arnem