<div dir="ltr"><div class="gmail_quote"><div dir="ltr">On Thu, Nov 8, 2018 at 6:41 AM "Alberto F. Martín" via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div text="#000000" bgcolor="#FFFFFF">
Dear Mark,<br>
<br>
thanks for your quick and comprehensive reply. <br>
<br>
Before moving to the results of the experiments that u suggested,
let me clarify two points<br>
on my original e-mail and your answer: <br>
<br>
(1) The raw timings and #iters. provided in my first e-mail were
actually <br>
obtained with "-pc_gamg_square_graph 1" (and not 0); sorry
about that, my mistake. <br>
(the logs, though, were consistent with the solver
configuration provided).<br>
The raw figures with "-pc_gamg_square_graph 0" are actually as
follows:<br>
<br>
(load3): [0.25074561, 0.3650926566, 0.6251466936,
0.8709517661, 15.52180776] <br>
(load3): [0.148803731, 0.325266364, 0.5538515123,
0.7537377281, 1.475100923]<br>
(load3): [8, 9, 11, 12, 12]<br>
<br>
Bottom line: significant improvement of absolute times for the
first 4x problems, marginal improvement for <br>
the largest problem (compared to
"-pc_gamg_square_graph 1")<br>
<br>
(2) <<<i>The PC setup times are large (I see 48 seconds at 16K
but you report 16). </i><i><br>
</i><i> -pc_gamg_square_graph 10 should help that.</i>>><br>
<br>
This disagreement is justified by the following note on my
original e-mail:<br>
<br>
<<<i>Please note that within each run, I execute
these two stages up-to</i><i><br>
</i><i> three times, and this influences absolute
timings given in -log_view.</i>>><br>
<br>
I tried new configurations based on your suggestions. Find attached
the results.<br>
(legends indicate changes with respect to the solver configuration
provided <br>
in my first e-mail).<br>
<br>
Bottom lines: (1) the configuration provided in my original e-mail
leads to fastest execution<br>
and less number of iteration for the first 4x problems. (2) <b>The
(new) parameter-value combinations</b><b><br>
</b><b>suggested seem to have almost no impact into the preconditioner
set up time of the last problem.</b></div></blockquote><div><br></div><div>Mark, could this bad setup just be non-scalability in ParMetis? How do we see the ParMetis time?</div><div><br></div><div> Thanks,</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 text="#000000" bgcolor="#FFFFFF"><b><br>
</b>I also tried HYPRE-BoomerAMG as suggested, with two different
configurations. <br>
<br>
*** SYMMETRIC CONFIGURATION ***<br>
-ksp_type cg<br>
-ksp_monitor<br>
-ksp_rtol 1.0e-6<br>
-ksp_converged_reason<br>
-ksp_max_it 500<br>
-ksp_norm_type unpreconditioned<br>
-ksp_view<br>
-log_view<br>
<br>
-pc_type hypre<br>
-pc_hypre_type boomeramg<br>
-pc_hypre_boomeramg_print_statistics 1<br>
-pc_hypre_boomeramg_strong_threshold 0.25<br>
-pc_hypre_boomeramg_coarsen_type HMIS<br>
-pc_hypre_boomeramg_relax_type_down symmetric-SOR/Jacobi<br>
-pc_hypre_boomeramg_relax_type_up symmetric-SOR/Jacobi<br>
-pc_hypre_boomeramg_relax_type_coarse Gaussian-elimination<br>
<br>
*** UNSYMMETRIC CONFIGURATION ***<br>
-ksp_type gmres<br>
-ksp_gmres_restart 500<br>
-ksp_monitor<br>
-ksp_rtol 1.0e-6<br>
-ksp_converged_reason<br>
-ksp_max_it 500<br>
-ksp_pc_side right<br>
-ksp_norm_type unpreconditioned<br>
<br>
-pc_type hypre<br>
-pc_hypre_type boomeramg<br>
-pc_hypre_boomeramg_print_statistics 1<br>
-pc_hypre_boomeramg_strong_threshold 0.25<br>
-pc_hypre_boomeramg_coarsen_type HMIS<br>
-pc_hypre_boomeramg_relax_type_down SOR/Jacobi<br>
-pc_hypre_boomeramg_relax_type_up SOR/Jacobi<br>
-pc_hypre_boomeramg_relax_type_coarse Gaussian-elimination<br>
<br>
The raw results were:<br>
<br>
*** SYMMETRIC CONFIGURATION ***<br>
<br>
(load3): [0.1828534687, 0.3055133289, 0.3582984209, 0.4280304033,
1.343549139]<br>
(load3): [0.2102472978, 0.4572948301, 0.7153297188, 0.9989531627,
N/A]<br>
(load3): [19, 23, 26, 28, 'DIVERGED_INDEFINITE_PC']<br>
<br>
*** UNSYMMETRIC CONFIGURATION ***<br>
<br>
(load3): [0.1841227429, 0.3082743008, 0.3652294828, 0.4654760892,
1.331299786]<br>
(load3): [0.1194557019, 0.2830136018, 0.5046830242, 1.363314636,
N/A]<br>
(load3): [15, 19, 24, 48, DIVERGED_ITS]<br>
<br>
Thus, the largest problem also seems to cause (even more severe)
issues to HYPRE, in particular,<br>
INDEFINITE PRECONDITIONER with CG, and not convergence within 500
iterations for GMRES. <br>
The preconditioner set up stage time, though, scales reasonably well
with the same data distribution<br>
that we used to feed GAMG (although the preconditioner computed for
the largest problem seems to be <br>
totally useless). <br>
<br>
I have logs for all these results if required.<br>
<br>
Thanks for your help!<br>
Best regards,<br>
Alberto.<br>
<br>
<br>
<br>
<div class="m_302126106648730347moz-cite-prefix">On 07/11/18 19:46, Mark Adams wrote:<br>
</div>
<blockquote type="cite">
<div dir="ltr">
<div dir="ltr">
<div dir="ltr">First I would add -gamg_est_ksp_type cg</div>
<div dir="ltr"><br>
</div>
<div>You seem to be converging well so I assume you are
setting the null space for GAMG.</div>
<div><br>
</div>
<div>Note, you should test hypre also.</div>
<div><br>
</div>
<div>You probably want a bigger "-pc_gamg_process_eq_limit
50". 200 at least but you test your machine with a range on
the largest problem. This is a parameter for reducing the
number of active processors (on coarse grids).</div>
<div><br>
</div>
<div>I would only worry about "load3". This has 16K equations
per process, which is where you start noticing "strong
scaling" problems, depending on the machine.</div>
<div><br>
</div>
<div>An important parameter is "-pc_gamg_square_graph 0". I
would probably start with infinity (eg, 10).</div>
<div><br>
</div>
<div>Now, I'm not sure about your domain, problem sizes, and
thus the weak scaling design. You seem to be scaling on the
background mesh, but that may not be a good proxy for
complexity. </div>
<div><br>
</div>
<div>You can look at the number of flops and scale it
appropriately by the number of solver iterations to get a
relative size of the problem. I would recommend scaling the
number of processors with this. For instance here the
MatMult line for the 4 proc and 16K proc run:</div>
<div>
<div><font face="monospace, monospace"><br>
</font></div>
<div><font face="monospace, monospace">------------------------------------------------------------------------------------------------------------------------</font></div>
<div><font face="monospace, monospace">Event
Count Time (sec) Flop
--- Global --- --- Stage --- Total</font></div>
<div><font face="monospace, monospace">
Max Ratio Max Ratio Max Ratio Mess Avg len
Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s</font></div>
<div><font face="monospace, monospace">------------------------------------------------------------------------------------------------------------------------</font></div>
<div><font face="monospace, monospace">MatMult
636 1.0 1.9035e-01 1.0 3.12e+08 1.1 7.6e+03 3.0e+03
0.0e+00 0 47 62 44 0 0 47 62 44 0 6275 [2 procs]</font></div>
<div><font face="monospace, monospace">MatMult
1416 1.0 1.9601e+00<font color="#ff0000">2744.6</font>
4.82e+08 <font color="#00ff00">0.0</font> 4.3e+08
7.2e+02 0.0e+00 0 48 50 48 0 0 48 50 48 0 2757975
[16K procs]</font></div>
</div>
<div><br>
</div>
<div>Now, you have empty processors. See the massive load <font color="#ff0000">imbalance</font> on time and the <font color="#00ff00">zero</font> on Flops. The "Ratio" is
max/min and cleary min=0 so PETSc reports a ratio of 0 (it
is infinity really).</div>
<div><br>
</div>
<div>Also, weak scaling on a thin body (I don't know your
domain) is a little funny because as the problem scales up
the mesh becomes more 3D and this causes the cost per
equation to go up. That is why I prefer to use the number of
non-zeros as the processor scaling function but number of
equations is easier ...</div>
<div><br>
</div>
<div>
<div>The PC setup times are large (I see 48 seconds at 16K
bu you report 16). -pc_gamg_square_graph 10 should help
that.</div>
<br class="m_302126106648730347gmail-Apple-interchange-newline">
</div>
<div>The max number of flops per processor in MatMult goes up
by 50% and the max time goes up by 10x and the number of
iterations goes up by 13/8. If I put all of this together I
get that 75% of the time at 16K is in communication at 16K.
I think that and the absolute time can be improved some by
optimizing parameters as I've suggested.</div>
<div><br>
</div>
<div>Mark</div>
<div><font face="monospace, monospace"><br>
</font></div>
<div><font face="monospace, monospace"><br>
</font></div>
<div><font face="monospace, monospace"><br>
</font></div>
<div><br>
</div>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr">On Wed, Nov 7, 2018 at 11:03 AM "Alberto F.
Martín" via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div text="#000000" bgcolor="#FFFFFF"> Dear All,<br>
<br>
we are performing a weak scaling test of the PETSc (v3.9.0)
GAMG preconditioner when applied to the linear system
arising<br>
from the <b>conforming unfitted FE discretization </b>(using
Q1 Lagrangian FEs) of a 3D PDE Poisson problem, where <br>
the boundary of the domain (a popcorn flake) is described
as a zero-level-set embedded within a uniform background <br>
(Cartesian-like) hexahedral mesh. Details underlying the FEM
formulation can be made available on demand if you <br>
believe that this might be helpful, but let me just point
out that it is designed such that it addresses the
well-known<br>
ill-conditioning issues of unfitted FE discretizations due
to the small cut cell problem. <br>
<br>
The weak scaling test is set up as follows. We start from a
single cube background mesh, and refine it uniformly several<br>
steps, until we have approximately either 10**3 (load1),
20**3 (load2), or 40**3 (load3) hexahedra/MPI task when <br>
distributing it over 4 MPI tasks. The benchmark is scaled
such that the next larger scale problem to be tested is
obtained<br>
by uniformly refining the mesh from the previous scale and
running it on 8x times the number of MPI tasks that we used<br>
in the previous scale. As a result, we obtain three weak
scaling curves for each of the three fixed loads per MPI
task<br>
above, on the following total number of MPI tasks: 4, 32,
262, 2097, 16777. The underlying mesh is not partitioned
among <br>
MPI tasks using ParMETIS (unstructured multilevel graph
partitioning) nor optimally by hand, but following the
so-called <br>
z-shape space-filling curves provided by an underlying
octree-like mesh handler (i.e., p4est library).<br>
<br>
I configured the preconditioned linear solver as follows:<br>
<br>
-ksp_type cg<br>
-ksp_monitor<br>
-ksp_rtol 1.0e-6<br>
-ksp_converged_reason<br>
-ksp_max_it 500<br>
-ksp_norm_type unpreconditioned<br>
-ksp_view<br>
-log_view<br>
<br>
-pc_type gamg<br>
-pc_gamg_type agg<br>
-mg_levels_esteig_ksp_type cg<br>
-mg_coarse_sub_pc_type cholesky<br>
-mg_coarse_sub_pc_factor_mat_ordering_type nd<br>
-pc_gamg_process_eq_limit 50<br>
-pc_gamg_square_graph 0<br>
-pc_gamg_agg_nsmooths 1<br>
<br>
Raw timings (in seconds) of the preconditioner set up and
PCG iterative solution stage, and number of iterations are
as follows:<br>
<br>
**preconditioner set up**<br>
(load1): [0.02542160451, 0.05169247743, 0.09266782179,
0.2426272957, 13.64161944]<br>
(load2): [0.1239175797 , 0.1885528499 , 0.2719282564 ,
0.4783878336, 13.37947339]<br>
(load3): [0.6565349903 , 0.9435049873 , 1.299908397 ,
1.916243652 , 16.02904088]<br>
<br>
**PCG stage**<br>
(load1): [0.003287350759, 0.008163803257, 0.03565631993,
0.08343045413, 0.6937994603]<br>
(load2): [0.0205939794 , 0.03594723623 , 0.07593298424,
0.1212046621 , 0.6780373845]<br>
(load3): [0.1310882876 , 0.3214917686 , 0.5532023879
, 0.766881627 , 1.485446003]<br>
<br>
**number of PCG iterations**<br>
(load1): [5, 8, 11, 13, 13]<br>
(load2): [7, 10, 12, 13, 13]<br>
(load3): [8, 10, 12, 13, 13]<br>
<br>
It can be observed that both the number of linear solver
iterations and the PCG stage timings (weakly) <br>
scale remarkably, but t<b>here is a significant time
increase when scaling the problem from 2097 to 16777 MPI
tasks </b><b><br>
</b><b>for the preconditioner setup stage</b> (e.g.,
1.916243652 vs 16.02904088 sec. with 40**3 cells per MPI
task).<br>
I gathered the combined output of -ksp_view and -log_view
(only) for all the points involving the load3 weak scaling<br>
test (find them attached to this message). Please note that
within each run, I execute the these two stages up-to<br>
three times, and this influences absolute timings given in
-log_view.<br>
<br>
Looking at the output of -log_view, it is very strange to
me, e.g., that the stage labelled as "Graph" <br>
does not scale properly as it is just a call to MatDuplicate
if the block size of the matrix is 1 (our case), and<br>
I guess that it is just a local operation that does not
require any communication.<br>
What I am missing here? The load does not seem to be
unbalanced looking at the "Ratio" column.<br>
<br>
I wonder whether the observed behaviour is as expected, or
this a miss-configuration of the solver from our side.<br>
I played (quite a lot) with several parameter-value
combinations, and the configuration above is the one that
led to fastest <br>
execution (from the ones tested, that might be incomplete,
I can also provide further feedback if helpful).<br>
Any feedback that we can get from your experience in order
to find the cause(s) of this issue and a mitigating solution<br>
will be of high added value.<br>
<br>
Thanks very much in advance!<br>
Best regards,<br>
Alberto.<br>
<pre class="m_302126106648730347m_1687720227499487021moz-signature" cols="72">--
Alberto F. Martín-Huertas
Senior Researcher, PhD. Computational Science
Centre Internacional de Mètodes Numèrics a l'Enginyeria (CIMNE)
Parc Mediterrani de la Tecnologia, UPC
Esteve Terradas 5, Building C3, Office 215,
08860 Castelldefels (Barcelona, Spain)
Tel.: (+34) 9341 34223
<a class="m_302126106648730347m_1687720227499487021moz-txt-link-abbreviated" href="mailto:e-mail:amartin@cimne.upc.edu" target="_blank">e-mail:amartin@cimne.upc.edu</a>
FEMPAR project co-founder
web: <a class="m_302126106648730347m_1687720227499487021moz-txt-link-freetext" href="http://www.fempar.org" target="_blank">http://www.fempar.org</a>
________________
IMPORTANT NOTICE
All personal data contained on this mail will be processed confidentially and registered in a file property of CIMNE in
order to manage corporate communications. You may exercise the rights of access, rectification, erasure and object by
letter sent to Ed. C1 Campus Norte UPC. Gran Capitán s/n Barcelona.
</pre>
</div>
</blockquote>
</div>
</blockquote>
<br>
<pre class="m_302126106648730347moz-signature" cols="72">--
Alberto F. Martín-Huertas
Senior Researcher, PhD. Computational Science
Centre Internacional de Mètodes Numèrics a l'Enginyeria (CIMNE)
Parc Mediterrani de la Tecnologia, UPC
Esteve Terradas 5, Building C3, Office 215,
08860 Castelldefels (Barcelona, Spain)
Tel.: (+34) 9341 34223
<a class="m_302126106648730347moz-txt-link-abbreviated" href="mailto:e-mail:amartin@cimne.upc.edu" target="_blank">e-mail:amartin@cimne.upc.edu</a>
FEMPAR project co-founder
web: <a class="m_302126106648730347moz-txt-link-freetext" href="http://www.fempar.org" target="_blank">http://www.fempar.org</a>
________________
IMPORTANT NOTICE
All personal data contained on this mail will be processed confidentially and registered in a file property of CIMNE in
order to manage corporate communications. You may exercise the rights of access, rectification, erasure and object by
letter sent to Ed. C1 Campus Norte UPC. Gran Capitán s/n Barcelona.
</pre>
</div>
</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>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><div><br></div><div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>