<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="gmail-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">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_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_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_1687720227499487021moz-txt-link-freetext" href="http://www.fempar.org" target="_blank">http://www.fempar.org</a>
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</pre>
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