[petsc-users] Guidance on GAMG preconditioning
Matthew Knepley
knepley at gmail.com
Sat Jun 6 19:21:03 CDT 2015
On Sat, Jun 6, 2015 at 6:02 PM, Young, Matthew, Adam <may at bu.edu> wrote:
> This is a problem from ionospheric plasma physics. The simulation treats
> ions via a particle-in-cell method and electrons as an inertialess fluid,
> the justification being that ionospheric ions are 10^4 times more massive
> than electrons. We further assume that the plasma is effectively neutral on
> the length scale of interest (i.e. quasi-neutral) and those assumptions
> allows us to write an elliptic equation for the electrostatic potential,
> phi: Div[n(x) T Grad(phi)]. n(x) is the quasi-neutral plasma density,
> which is updated via an ion gather at each time step, and T is a tensor of
> constant coefficients that looks like {{1, kappa, 0},{-kappa, 1, 0},{0, 0,
> 1+kappa^2}}, where kappa is the ratio of gyrofrequency to collision
> frequency for electrons (~100 for our problem)*. The RHS is a function of
> density, ion current (or flux, both of which are related to density), and
> constant electron fluid parameters. Eq 1 of the attached paper shows this
> equation for the 2-D problem in the plane perpendicular to the ambient
> magnetic field.
>
Its hard to say anything without knowing what the n(x) functions look like.
I would say now that it is easy to try GAMG, so
that is what I would do first.
Thanks,
Matt
> --Matt
>
> *It was a little unfair of me to say earlier that the off-diagonal terms
> grow as the simulation progresses. It's the density that gradients grow and
> they are multiplied by kappa.
>
>
>
> --------------------------------------------------------------
> Matthew Young
> Graduate Student
> Boston University Dept. of Astronomy
> --------------------------------------------------------------
>
> ------------------------------
> *From:* Matthew Knepley [knepley at gmail.com]
> *Sent:* Saturday, June 06, 2015 6:12 PM
> *To:* Young, Matthew, Adam
> *Cc:* Justin Chang; Mark Adams; petsc-users
>
> *Subject:* Re: [petsc-users] Guidance on GAMG preconditioning
>
> 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
>
>
>> --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
>
--
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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