[petsc-users] Guidance on GAMG preconditioning

[Young, Matthew, Adam]

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?

--Matt

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Matthew Young
Graduate Student
Boston University Dept. of Astronomy
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________________________________
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<mailto: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

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