[petsc-users] Guidance on GAMG preconditioning

Matthew Knepley knepley at gmail.com
Sat Jun 6 17:12:38 CDT 2015

On Sat, Jun 6, 2015 at 3:00 PM, Young, Matthew, Adam <may at bu.edu> wrote:

>  Forgive me for being like a child who wanders into the middle of a
> movie...
>  I've been attempting to follow this conversation from a beginner's level
> because I am trying to solve an elliptic PDE with variable coefficients.
> Both the operator and the RHS change at each time step and the operator has
> off-diagonal terms that become dominant as the instability of interest
> grows. I read somewhere that a direct method is the best for this but I'm
> intrigued by Justin's comment that GAMG seems to be "the preconditioner to
> use for elliptic problems". I don't want to highjack this conversation but
> it seems like a good chance to ask for your collective advice on resources
> for understanding my problem. Any thoughts?

The problem here is that fast methods do not depend on the operator being
elliptic so much as they depend on the operator
falling off away from the diagonal (satisfying a Calderon-Zygmund bound,
there are lots of ways of expressing this). When
this ceases to be true, these methods stop being fast.

So the answer is, when you have complicated coefficient structure, there
are no general methods and you need to know more
about exactly what is going on. Where is your problem from?


> --Matt
>   --------------------------------------------------------------
> Matthew Young
> Graduate Student
> Boston University Dept. of Astronomy
> --------------------------------------------------------------
>    ------------------------------
> *From:* petsc-users-bounces at mcs.anl.gov [petsc-users-bounces at mcs.anl.gov]
> on behalf of Justin Chang [jychang48 at gmail.com]
> *Sent:* Saturday, June 06, 2015 5:29 AM
> *To:* Mark Adams
> *Cc:* petsc-users
> *Subject:* Re: [petsc-users] Guidance on GAMG preconditioning
>   Matt and Mark thank you guys for your responses.
> The reason I brought up GAMG was because it seems to me that this is the
> preconditioner to use for elliptic problems. However, I am using CG/Jacobi
> for my larger problems and the solver converges (with -ksp_atol and
> -ksp_rtol set to 1e-8). Using GAMG I get rough the same wall-clock time,
> but significantly fewer solver iterations.
> As I also kind of mentioned in another mail, the ultimate purpose is to
> compare how this "correction" methodology using the TAO solver (with
> bounded constraints) performs compared to the original methodology using
> the KSP solver (without constraints). I have the A for BLMVM and CG/Jacobi
> and they are roughly 0.3 and 0.2 respectively (do these sound about
> right?). Although the AI is higher for TAO , the ratio of actual FLOPS/s
> over the AI*STREAMS BW is smaller, though I am not sure what conclusions to
> make of that. This was also partly why I wanted to see what kind of metrics
> another KSP solver/preconditioner produces.
>  Point being, if I were to draw such comparisons between TAO and KSP,
> would I get crucified if people find out I am using CG/Jacobi and not GAMG?
>  Thanks,
> Justin
> On Fri, Jun 5, 2015 at 2:02 PM, Mark Adams <mfadams at lbl.gov> wrote:
>>>  The overwhleming cost of AMG is the Galerkin triple-product RAP.
>>  That is overstating it a bit.  It can be if you have a hard 3D operator
>> and coarsening slowly is best.
>>  Rule of thumb is you spend 50% time is the solver and 50% in the setup,
>> which is often mostly RAP (in 3D, 2D is much faster).  That way you are
>> within 2x of optimal and it often works out that way anyway.
>>  Mark

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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