<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">On Sat, Jun 6, 2015 at 3:00 PM, Young, Matthew, Adam <span dir="ltr"><<a href="mailto:may@bu.edu" target="_blank">may@bu.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<div><font size="2">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?</font></div></div></div></blockquote><div><br></div><div>The problem here is that fast methods do not depend on the operator being elliptic so much as they depend on the operator</div><div>falling off away from the diagonal (satisfying a Calderon-Zygmund bound, there are lots of ways of expressing this). When</div><div>this ceases to be true, these methods stop being fast.</div><div><br></div><div>So the answer is, when you have complicated coefficient structure, there are no general methods and you need to know more</div><div>about exactly what is going on. Where is your problem from?</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div style="direction:ltr;font-family:Tahoma;color:#000000;font-size:10pt">
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<div>Matthew Young</div>
<div>Graduate Student</div>
<div>Boston University Dept. of Astronomy</div>
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<div style="direction:ltr"><font face="Tahoma" size="2" color="#000000"><b>From:</b> <a href="mailto:petsc-users-bounces@mcs.anl.gov" target="_blank">petsc-users-bounces@mcs.anl.gov</a> [<a href="mailto:petsc-users-bounces@mcs.anl.gov" target="_blank">petsc-users-bounces@mcs.anl.gov</a>] on behalf of Justin Chang [<a href="mailto:jychang48@gmail.com" target="_blank">jychang48@gmail.com</a>]<br>
<b>Sent:</b> Saturday, June 06, 2015 5:29 AM<br>
<b>To:</b> Mark Adams<br>
<b>Cc:</b> petsc-users<br>
<b>Subject:</b> Re: [petsc-users] Guidance on GAMG preconditioning<br>
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<div dir="ltr">Matt and Mark thank you guys for your responses. <br>
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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. <br>
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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.
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<div>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? <br>
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<div>Thanks,<br>
Justin</div>
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<div class="gmail_quote">On Fri, Jun 5, 2015 at 2:02 PM, Mark Adams <span dir="ltr">
<<a href="mailto:mfadams@lbl.gov" target="_blank">mfadams@lbl.gov</a>></span> wrote:<br>
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<div>The overwhleming cost of AMG is the Galerkin triple-product RAP.</div>
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<div>That is overstating it a bit. It can be if you have a hard 3D operator and coarsening slowly is best.</div>
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<div>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.</div>
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</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div>
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