[petsc-users] Convergence of AMG

Manav Bhatia bhatiamanav at gmail.com
Tue Oct 30 10:32:06 CDT 2018 


> On Oct 29, 2018, at 4:07 PM, Mark Adams <mfadams at lbl.gov> wrote:
> 
> * the two level results tell us that MG is not doing well on the coarse grids. So the coarse grids are the problem.
> 
> * Do not worry about timing now. Get the math correct. The two level solve is not meant to be a solution just a diagnostic so don't try to optimize it by squaring the graph. Use -pc_gamg_square_graph 0.
> 
> * It looks like you don't need 4 smoothing steps but lets keep it and we can dial it back later.
> 
> * This table is interesting. First, you had about 12 iterations earlier and I think your rtol was tighter than the default (so the iteration could should go down not up). Do you know what change here?

I maintained the same tolerance using -ksp_rtol 1.e-8 (did not copy this into the parameter list in the previous email). 

The 2 level iterations was a typo and should have been 12.  I have corrected the table here: 
-mg_levels_ksp_max_it 4 -pc_gamg_square_graph 1 -pc_gamg_threshold 0. -ksp_rtol 1.e-8

Case#  |  #levels   |    #KSP Iters
——————————————
     1      |     2         |       12
     2      |     3         |       18
     3      |     4         |       40
     4      |     5         |       59


> 
> Note, even though -mg_levels_ksp_max_it is not in the ksp_view it does work. It is syntactic sugar to just add it to all levels like you did manually.
> 
> Anyway, these number look reasonable. It is interesting that 3 levels ran well but the 4th level ran poorly. This implies we want to slow down coarsening on these levels, but ...
> 
> First can you please rerun this experiment with -pc_gamg_square_graph 0.
> 

Following is the summary of the results with -pc_gamg_square_graph 0

-mg_levels_ksp_max_it 4 -pc_gamg_square_graph 0 -pc_gamg_threshold 0. -ksp_rtol 1.e-8

Case#  |  #levels   |    #KSP Iters
——————————————
     5      |     2        |         9
     6      |     3        |       13
     7      |     4        |       31
     8      |     5        |       50


> Also, please run with -info. This is very noisy but you can grep on "GAMG" and send that output to us (about 15 lines).

I have included information about all 8 cases below. 

Thanks for your help! 

-Manav

> 
> Thanks,
> Mark
> 
> 


Case 1)  -mg_levels_ksp_max_it 4 -pc_gamg_square_graph 1 -pc_gamg_threshold 0. -ksp_rtol 1.e-8 -pc_mg_levels 2 
Dhcp-90-164:tmp manav$ cat t | grep "KSP\ Res"
    0 KSP Residual norm 2.980759132912e+01 
    1 KSP Residual norm 1.268404746671e+00 
    2 KSP Residual norm 1.420311012425e-01 
    3 KSP Residual norm 3.026536678757e-02 
    4 KSP Residual norm 6.511170312990e-03 
    5 KSP Residual norm 1.539620841789e-03 
    6 KSP Residual norm 3.655528499924e-04 
    7 KSP Residual norm 8.111524453985e-05 
    8 KSP Residual norm 1.995956470679e-05 
    9 KSP Residual norm 4.397662980825e-06 
   10 KSP Residual norm 9.636956929325e-07 
   11 KSP Residual norm 3.013384202118e-07 
   12 KSP Residual norm 1.867699579372e-07 
Dhcp-90-164:tmp manav$ cat t | grep GAMG
[0] PCSetUp_GAMG(): level 0) N=543606, n data rows=6, n data cols=6, nnz/row (ave)=54, np=4
[0] PCGAMGFilterGraph(): 	 98.7979% nnz after filtering, with threshold 0., 8.95943 nnz ave. (N=90601)
[0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 1 to square
[0] PCGAMGProlongator_AGG(): New grid 6837 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.748254e+00 min=6.352623e-02 PC=jacobi
[0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 10296 with simple aggregation
[0] PCSetUp_GAMG(): 1) N=41022, n data cols=6, nnz/row (ave)=69, 1 active pes
[0] PCSetUp_GAMG(): 2 levels, grid complexity = 1.0976


Case 2)  -mg_levels_ksp_max_it 4 -pc_gamg_square_graph 1 -pc_gamg_threshold 0. -ksp_rtol 1.e-8 -pc_mg_levels 3 
Dhcp-90-164:tmp manav$ cat t | grep "KSP\ Res"
    0 KSP Residual norm 1.721859579323e+01 
    1 KSP Residual norm 2.372150715400e+00 
    2 KSP Residual norm 4.332444773735e-01 
    3 KSP Residual norm 1.828644450393e-01 
    4 KSP Residual norm 6.508336322670e-02 
    5 KSP Residual norm 2.352085101499e-02 
    6 KSP Residual norm 9.165114885090e-03 
    7 KSP Residual norm 3.674781085969e-03 
    8 KSP Residual norm 1.331249870878e-03 
    9 KSP Residual norm 4.566260302483e-04 
   10 KSP Residual norm 1.795556967223e-04 
   11 KSP Residual norm 6.793314859559e-05 
   12 KSP Residual norm 2.504121594312e-05 
   13 KSP Residual norm 9.167163291488e-06 
   14 KSP Residual norm 3.283556007932e-06 
   15 KSP Residual norm 1.277586362108e-06 
   16 KSP Residual norm 4.852580652992e-07 
   17 KSP Residual norm 1.901791545937e-07 
   18 KSP Residual norm 7.974015462515e-08 
Dhcp-90-164:tmp manav$ cat t | grep GAMG
[0] PCSetUp_GAMG(): level 0) N=543606, n data rows=6, n data cols=6, nnz/row (ave)=54, np=4
[0] PCGAMGFilterGraph(): 	 98.7979% nnz after filtering, with threshold 0., 8.95943 nnz ave. (N=90601)
[0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 1 to square
[0] PCGAMGProlongator_AGG(): New grid 6837 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.748254e+00 min=6.352623e-02 PC=jacobi
[0] PCSetUp_GAMG(): 1) N=41022, n data cols=6, nnz/row (ave)=69, 4 active pes
[0] PCGAMGFilterGraph(): 	 100.% nnz after filtering, with threshold 0., 11.6521 nnz ave. (N=6837)
[0] PCGAMGProlongator_AGG(): New grid 1121 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=1.785527e+00 min=6.042089e-02 PC=jacobi
[0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 1656 with simple aggregation
[0] PCSetUp_GAMG(): 2) N=6726, n data cols=6, nnz/row (ave)=140, 1 active pes
[0] PCSetUp_GAMG(): 3 levels, grid complexity = 1.12982


Case 3)  -mg_levels_ksp_max_it 4 -pc_gamg_square_graph 1 -pc_gamg_threshold 0. -ksp_rtol 1.e-8 -pc_mg_levels 4 
Dhcp-90-164:tmp manav$ cat t | grep "KSP\ Res"
    0 KSP Residual norm 5.715310219090e+00 
    1 KSP Residual norm 1.702306568500e+00 
    2 KSP Residual norm 1.105404714191e+00 
    3 KSP Residual norm 7.521070321363e-01 
    4 KSP Residual norm 5.151770148497e-01 
    5 KSP Residual norm 3.407231098045e-01 
    6 KSP Residual norm 2.154066019733e-01 
    7 KSP Residual norm 1.320975463963e-01 
    8 KSP Residual norm 8.464181469022e-02 
    9 KSP Residual norm 5.404783722947e-02 
   10 KSP Residual norm 3.571728349786e-02 
   11 KSP Residual norm 2.363141413294e-02 
   12 KSP Residual norm 1.530000070717e-02 
   13 KSP Residual norm 9.398576202667e-03 
   14 KSP Residual norm 5.389891497192e-03 
   15 KSP Residual norm 3.308851504727e-03 
   16 KSP Residual norm 2.233599324934e-03 
   17 KSP Residual norm 1.471510415641e-03 
   18 KSP Residual norm 9.214853138234e-04 
   19 KSP Residual norm 6.090808616289e-04 
   20 KSP Residual norm 4.205193238717e-04 
   21 KSP Residual norm 2.728384192436e-04 
   22 KSP Residual norm 1.647370935175e-04 
   23 KSP Residual norm 1.007397471037e-04 
   24 KSP Residual norm 6.133965622058e-05 
   25 KSP Residual norm 3.650073757918e-05 
   26 KSP Residual norm 2.220817401390e-05 
   27 KSP Residual norm 1.423846811011e-05 
   28 KSP Residual norm 9.147106610671e-06 
   29 KSP Residual norm 5.622102212398e-06 
   30 KSP Residual norm 3.427704849314e-06 
   31 KSP Residual norm 2.562333599882e-06 
   32 KSP Residual norm 1.780393486817e-06 
   33 KSP Residual norm 1.175933486658e-06 
   34 KSP Residual norm 7.633724873183e-07 
   35 KSP Residual norm 4.635656121553e-07 
   36 KSP Residual norm 2.809545347534e-07 
   37 KSP Residual norm 1.736631971561e-07 
   38 KSP Residual norm 1.074049251439e-07 
   39 KSP Residual norm 6.374646169363e-08 
   40 KSP Residual norm 4.140669801911e-08 
Dhcp-90-164:tmp manav$ cat t | grep GAMG
[0] PCSetUp_GAMG(): level 0) N=543606, n data rows=6, n data cols=6, nnz/row (ave)=54, np=4
[0] PCGAMGFilterGraph(): 	 98.7979% nnz after filtering, with threshold 0., 8.95943 nnz ave. (N=90601)
[0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 1 to square
[0] PCGAMGProlongator_AGG(): New grid 6837 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.748254e+00 min=6.352623e-02 PC=jacobi
[0] PCSetUp_GAMG(): 1) N=41022, n data cols=6, nnz/row (ave)=69, 4 active pes
[0] PCGAMGFilterGraph(): 	 100.% nnz after filtering, with threshold 0., 11.6521 nnz ave. (N=6837)
[0] PCGAMGProlongator_AGG(): New grid 1121 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=1.785527e+00 min=6.042089e-02 PC=jacobi
[0] PCSetUp_GAMG(): 2) N=6726, n data cols=6, nnz/row (ave)=140, 4 active pes
[0] PCGAMGFilterGraph(): 	 100.% nnz after filtering, with threshold 0., 23.3696 nnz ave. (N=1121)
[0] PCGAMGProlongator_AGG(): New grid 107 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=3.003329e+00 min=8.421562e-02 PC=jacobi
[0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 144 with simple aggregation
[0] PCSetUp_GAMG(): 3) N=642, n data cols=6, nnz/row (ave)=154, 1 active pes
[0] PCSetUp_GAMG(): 4 levels, grid complexity = 1.13323


Case 4)  -mg_levels_ksp_max_it 4 -pc_gamg_square_graph 1 -pc_gamg_threshold 0. -ksp_rtol 1.e-8 -pc_mg_levels 5 
Dhcp-90-164:tmp manav$ cat t | grep "KSP\ Res"
    0 KSP Residual norm 1.796966525877e+00 
    1 KSP Residual norm 1.272395001001e+00 
    2 KSP Residual norm 9.587765774342e-01 
    3 KSP Residual norm 7.503468727302e-01 
    4 KSP Residual norm 5.929828008661e-01 
    5 KSP Residual norm 4.667907393525e-01 
    6 KSP Residual norm 3.582573847190e-01 
    7 KSP Residual norm 2.641549535092e-01 
    8 KSP Residual norm 1.897005575664e-01 
    9 KSP Residual norm 1.290185919854e-01 
   10 KSP Residual norm 8.674970372217e-02 
   11 KSP Residual norm 5.719457030929e-02 
   12 KSP Residual norm 3.670199440851e-02 
   13 KSP Residual norm 2.279854011416e-02 
   14 KSP Residual norm 1.413541409138e-02 
   15 KSP Residual norm 9.904419724774e-03 
   16 KSP Residual norm 7.479600408120e-03 
   17 KSP Residual norm 5.653470278882e-03 
   18 KSP Residual norm 4.357609222840e-03 
   19 KSP Residual norm 3.501603455533e-03 
   20 KSP Residual norm 2.740008551458e-03 
   21 KSP Residual norm 2.000305455177e-03 
   22 KSP Residual norm 1.465665578257e-03 
   23 KSP Residual norm 1.063641050628e-03 
   24 KSP Residual norm 7.320397918812e-04 
   25 KSP Residual norm 4.987179366244e-04 
   26 KSP Residual norm 3.531130935050e-04 
   27 KSP Residual norm 2.534997938742e-04 
   28 KSP Residual norm 1.815505756854e-04 
   29 KSP Residual norm 1.303047003006e-04 
   30 KSP Residual norm 9.159509138706e-05 
   31 KSP Residual norm 7.324246273743e-05 
   32 KSP Residual norm 5.465350505655e-05 
   33 KSP Residual norm 3.876661576537e-05 
   34 KSP Residual norm 2.792720150402e-05 
   35 KSP Residual norm 2.108207616943e-05 
   36 KSP Residual norm 1.611370701356e-05 
   37 KSP Residual norm 1.208049584171e-05 
   38 KSP Residual norm 9.075511243294e-06 
   39 KSP Residual norm 7.091514153440e-06 
   40 KSP Residual norm 5.623979353049e-06 
   41 KSP Residual norm 4.346769151236e-06 
   42 KSP Residual norm 3.197496840488e-06 
   43 KSP Residual norm 2.265919711506e-06 
   44 KSP Residual norm 1.600975191547e-06 
   45 KSP Residual norm 1.132335469737e-06 
   46 KSP Residual norm 7.710870825137e-07 
   47 KSP Residual norm 5.064951347280e-07 
   48 KSP Residual norm 3.448475289519e-07 
   49 KSP Residual norm 2.450120965032e-07 
   50 KSP Residual norm 1.826746152120e-07 
   51 KSP Residual norm 1.445084170865e-07 
   52 KSP Residual norm 1.200408904185e-07 
   53 KSP Residual norm 9.882182031280e-08 
   54 KSP Residual norm 7.914655725555e-08 
   55 KSP Residual norm 6.110632924313e-08 
   56 KSP Residual norm 4.632304250505e-08 
   57 KSP Residual norm 3.242693236988e-08 
   58 KSP Residual norm 2.195784301351e-08 
   59 KSP Residual norm 1.571496587971e-08 
Dhcp-90-164:tmp manav$ cat t | grep GAMG
[0] PCSetUp_GAMG(): level 0) N=543606, n data rows=6, n data cols=6, nnz/row (ave)=54, np=4
[0] PCGAMGFilterGraph(): 	 98.7979% nnz after filtering, with threshold 0., 8.95943 nnz ave. (N=90601)
[0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 1 to square
[0] PCGAMGProlongator_AGG(): New grid 6837 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.748254e+00 min=6.352623e-02 PC=jacobi
[0] PCSetUp_GAMG(): 1) N=41022, n data cols=6, nnz/row (ave)=69, 4 active pes
[0] PCGAMGFilterGraph(): 	 100.% nnz after filtering, with threshold 0., 11.6521 nnz ave. (N=6837)
[0] PCGAMGProlongator_AGG(): New grid 1121 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=1.785527e+00 min=6.042089e-02 PC=jacobi
[0] PCSetUp_GAMG(): 2) N=6726, n data cols=6, nnz/row (ave)=140, 4 active pes
[0] PCGAMGFilterGraph(): 	 100.% nnz after filtering, with threshold 0., 23.3696 nnz ave. (N=1121)
[0] PCGAMGProlongator_AGG(): New grid 107 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=3.003329e+00 min=8.421562e-02 PC=jacobi
[0] PCSetUp_GAMG(): 3) N=642, n data cols=6, nnz/row (ave)=154, 4 active pes
[0] PCGAMGFilterGraph(): 	 100.% nnz after filtering, with threshold 0., 24.5 nnz ave. (N=107)
[0] PCGAMGProlongator_AGG(): New grid 9 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.863578e+00 min=9.275407e-02 PC=jacobi
[0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 6 with simple aggregation
[0] PCSetUp_GAMG(): 4) N=54, n data cols=6, nnz/row (ave)=54, 1 active pes
[0] PCSetUp_GAMG(): 5 levels, grid complexity = 1.13333


Case 5)  -mg_levels_ksp_max_it 4 -pc_gamg_square_graph 0 -pc_gamg_threshold 0. -ksp_rtol 1.e-8 -pc_mg_levels 2 
Dhcp-90-164:tmp manav$ cat t | grep "KSP\ Res"
    0 KSP Residual norm 4.658748806834e+01 
    1 KSP Residual norm 6.825811660437e-01 
    2 KSP Residual norm 3.642264109013e-02 
    3 KSP Residual norm 2.013016230540e-03 
    4 KSP Residual norm 2.013432241615e-04 
    5 KSP Residual norm 2.105457376227e-05 
    6 KSP Residual norm 3.003346327786e-06 
    7 KSP Residual norm 1.445664726245e-06 
    8 KSP Residual norm 6.952678680043e-07 
    9 KSP Residual norm 3.813304720986e-07 
Dhcp-90-164:tmp manav$ cat t | grep GAMG
[0] PCSetUp_GAMG(): level 0) N=543606, n data rows=6, n data cols=6, nnz/row (ave)=54, np=4
[0] PCGAMGFilterGraph(): 	 98.7979% nnz after filtering, with threshold 0., 8.95943 nnz ave. (N=90601)
[0] PCGAMGProlongator_AGG(): New grid 16817 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.748254e+00 min=6.352623e-02 PC=jacobi
[0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 25260 with simple aggregation
[0] PCSetUp_GAMG(): 1) N=100902, n data cols=6, nnz/row (ave)=103, 1 active pes
[0] PCSetUp_GAMG(): 2 levels, grid complexity = 1.35717


Case 6)  -mg_levels_ksp_max_it 4 -pc_gamg_square_graph 0 -pc_gamg_threshold 0. -ksp_rtol 1.e-8 -pc_mg_levels 3 
Dhcp-90-164:tmp manav$ cat t | grep "KSP\ Res"
    0 KSP Residual norm 2.700027956285e+01 
    1 KSP Residual norm 2.081487493276e+00 
    2 KSP Residual norm 2.504352351366e-01 
    3 KSP Residual norm 7.222719417818e-02 
    4 KSP Residual norm 1.769085428189e-02 
    5 KSP Residual norm 4.200829546873e-03 
    6 KSP Residual norm 1.100496697039e-03 
    7 KSP Residual norm 2.880192907717e-04 
    8 KSP Residual norm 7.621296303148e-05 
    9 KSP Residual norm 1.923264828609e-05 
   10 KSP Residual norm 4.962521087771e-06 
   11 KSP Residual norm 1.223640145242e-06 
   12 KSP Residual norm 3.668999985201e-07 
   13 KSP Residual norm 1.828878545694e-07 
Dhcp-90-164:tmp manav$ cat t | grep GAMG
[0] PCSetUp_GAMG(): level 0) N=543606, n data rows=6, n data cols=6, nnz/row (ave)=54, np=4
[0] PCGAMGFilterGraph(): 	 98.7979% nnz after filtering, with threshold 0., 8.95943 nnz ave. (N=90601)
[0] PCGAMGProlongator_AGG(): New grid 16817 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.748254e+00 min=6.352623e-02 PC=jacobi
[0] PCSetUp_GAMG(): 1) N=100902, n data cols=6, nnz/row (ave)=103, 4 active pes
[0] PCGAMGFilterGraph(): 	 100.% nnz after filtering, with threshold 0., 17.2399 nnz ave. (N=16817)
[0] PCGAMGProlongator_AGG(): New grid 2021 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=1.704298e+00 min=6.370030e-02 PC=jacobi
[0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 3006 with simple aggregation
[0] PCSetUp_GAMG(): 2) N=12126, n data cols=6, nnz/row (ave)=172, 1 active pes
[0] PCSetUp_GAMG(): 3 levels, grid complexity = 1.42875


Case 7)  -mg_levels_ksp_max_it 4 -pc_gamg_square_graph 0 -pc_gamg_threshold 0. -ksp_rtol 1.e-8 -pc_mg_levels 4 
Dhcp-90-164:tmp manav$ cat t | grep "KSP\ Res"
    0 KSP Residual norm 9.908487889752e+00 
    1 KSP Residual norm 2.252812343792e+00 
    2 KSP Residual norm 1.165408110334e+00 
    3 KSP Residual norm 6.434735893158e-01 
    4 KSP Residual norm 3.696466541726e-01 
    5 KSP Residual norm 2.135677187677e-01 
    6 KSP Residual norm 1.257757438010e-01 
    7 KSP Residual norm 7.128420785165e-02 
    8 KSP Residual norm 3.976090525850e-02 
    9 KSP Residual norm 2.279000353245e-02 
   10 KSP Residual norm 1.300701287311e-02 
   11 KSP Residual norm 7.498254128331e-03 
   12 KSP Residual norm 4.288501173737e-03 
   13 KSP Residual norm 2.316089581521e-03 
   14 KSP Residual norm 1.263802234905e-03 
   15 KSP Residual norm 7.296829650365e-04 
   16 KSP Residual norm 4.261675876945e-04 
   17 KSP Residual norm 2.440548986676e-04 
   18 KSP Residual norm 1.436965272125e-04 
   19 KSP Residual norm 8.010925146489e-05 
   20 KSP Residual norm 4.339850994759e-05 
   21 KSP Residual norm 2.411926753762e-05 
   22 KSP Residual norm 1.306205068099e-05 
   23 KSP Residual norm 7.542931204731e-06 
   24 KSP Residual norm 4.283178968440e-06 
   25 KSP Residual norm 2.483127922661e-06 
   26 KSP Residual norm 1.517894242402e-06 
   27 KSP Residual norm 8.801147250084e-07 
   28 KSP Residual norm 5.088326120723e-07 
   29 KSP Residual norm 2.732311721999e-07 
   30 KSP Residual norm 1.450174505696e-07 
   31 KSP Residual norm 9.861763824710e-08 
Dhcp-90-164:tmp manav$ cat t | grep GAMG
[0] PCSetUp_GAMG(): level 0) N=543606, n data rows=6, n data cols=6, nnz/row (ave)=54, np=4
[0] PCGAMGFilterGraph(): 	 98.7979% nnz after filtering, with threshold 0., 8.95943 nnz ave. (N=90601)
[0] PCGAMGProlongator_AGG(): New grid 16817 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.748254e+00 min=6.352623e-02 PC=jacobi
[0] PCSetUp_GAMG(): 1) N=100902, n data cols=6, nnz/row (ave)=103, 4 active pes
[0] PCGAMGFilterGraph(): 	 100.% nnz after filtering, with threshold 0., 17.2399 nnz ave. (N=16817)
[0] PCGAMGProlongator_AGG(): New grid 2021 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=1.704298e+00 min=6.370030e-02 PC=jacobi
[0] PCSetUp_GAMG(): 2) N=12126, n data cols=6, nnz/row (ave)=172, 4 active pes
[0] PCGAMGFilterGraph(): 	 100.% nnz after filtering, with threshold 0., 28.7325 nnz ave. (N=2021)
[0] PCGAMGProlongator_AGG(): New grid 161 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.212396e+00 min=1.149492e-01 PC=jacobi
[0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 204 with simple aggregation
[0] PCSetUp_GAMG(): 3) N=966, n data cols=6, nnz/row (ave)=176, 1 active pes
[0] PCSetUp_GAMG(): 4 levels, grid complexity = 1.43458


Case 8)  -mg_levels_ksp_max_it 4 -pc_gamg_square_graph 0 -pc_gamg_threshold 0. -ksp_rtol 1.e-8 -pc_mg_levels 5 
Dhcp-90-164:tmp manav$ cat t | grep "KSP\ Res"
    0 KSP Residual norm 2.218294876305e+00 
    1 KSP Residual norm 1.632572879485e+00 
    2 KSP Residual norm 1.182643328612e+00 
    3 KSP Residual norm 8.718741753444e-01 
    4 KSP Residual norm 6.533291909118e-01 
    5 KSP Residual norm 4.866483224152e-01 
    6 KSP Residual norm 3.484903886854e-01 
    7 KSP Residual norm 2.348475670124e-01 
    8 KSP Residual norm 1.537187403224e-01 
    9 KSP Residual norm 1.026536155589e-01 
   10 KSP Residual norm 6.824513463193e-02 
   11 KSP Residual norm 4.627422220135e-02 
   12 KSP Residual norm 3.117616798825e-02 
   13 KSP Residual norm 2.081871084553e-02 
   14 KSP Residual norm 1.460827781562e-02 
   15 KSP Residual norm 1.037979487427e-02 
   16 KSP Residual norm 6.886117836686e-03 
   17 KSP Residual norm 4.634120402061e-03 
   18 KSP Residual norm 2.822150912459e-03 
   19 KSP Residual norm 1.699261862470e-03 
   20 KSP Residual norm 1.127636890762e-03 
   21 KSP Residual norm 7.233233068369e-04 
   22 KSP Residual norm 4.545631018082e-04 
   23 KSP Residual norm 2.995811344995e-04 
   24 KSP Residual norm 1.984480794186e-04 
   25 KSP Residual norm 1.339576789380e-04 
   26 KSP Residual norm 8.964509794502e-05 
   27 KSP Residual norm 6.063175592350e-05 
   28 KSP Residual norm 4.271774591608e-05 
   29 KSP Residual norm 3.026766800790e-05 
   30 KSP Residual norm 2.191056439926e-05 
   31 KSP Residual norm 1.813101162702e-05 
   32 KSP Residual norm 1.410197450206e-05 
   33 KSP Residual norm 9.889952949347e-06 
   34 KSP Residual norm 6.488236898017e-06 
   35 KSP Residual norm 4.232064596117e-06 
   36 KSP Residual norm 2.736230796810e-06 
   37 KSP Residual norm 1.829705002417e-06 
   38 KSP Residual norm 1.272435477754e-06 
   39 KSP Residual norm 8.374839157107e-07 
   40 KSP Residual norm 5.423071251782e-07 
   41 KSP Residual norm 3.638843185090e-07 
   42 KSP Residual norm 2.318570275176e-07 
   43 KSP Residual norm 1.494263195512e-07 
   44 KSP Residual norm 1.014479883907e-07 
   45 KSP Residual norm 7.010792145263e-08 
   46 KSP Residual norm 5.302212871376e-08 
   47 KSP Residual norm 4.129998076695e-08 
   48 KSP Residual norm 3.174687615554e-08 
   49 KSP Residual norm 2.425058914303e-08 
   50 KSP Residual norm 1.810773091084e-08 
Dhcp-90-164:tmp manav$ cat t | grep GAMG
[0] PCSetUp_GAMG(): level 0) N=543606, n data rows=6, n data cols=6, nnz/row (ave)=54, np=4
[0] PCGAMGFilterGraph(): 	 98.7979% nnz after filtering, with threshold 0., 8.95943 nnz ave. (N=90601)
[0] PCGAMGProlongator_AGG(): New grid 16817 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.748254e+00 min=6.352623e-02 PC=jacobi
[0] PCSetUp_GAMG(): 1) N=100902, n data cols=6, nnz/row (ave)=103, 4 active pes
[0] PCGAMGFilterGraph(): 	 100.% nnz after filtering, with threshold 0., 17.2399 nnz ave. (N=16817)
[0] PCGAMGProlongator_AGG(): New grid 2021 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=1.704298e+00 min=6.370030e-02 PC=jacobi
[0] PCSetUp_GAMG(): 2) N=12126, n data cols=6, nnz/row (ave)=172, 4 active pes
[0] PCGAMGFilterGraph(): 	 100.% nnz after filtering, with threshold 0., 28.7325 nnz ave. (N=2021)
[0] PCGAMGProlongator_AGG(): New grid 161 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.212396e+00 min=1.149492e-01 PC=jacobi
[0] PCSetUp_GAMG(): 3) N=966, n data cols=6, nnz/row (ave)=176, 4 active pes
[0] PCGAMGFilterGraph(): 	 100.% nnz after filtering, with threshold 0., 28.2353 nnz ave. (N=161)
[0] PCGAMGProlongator_AGG(): New grid 14 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.257007e+00 min=1.166837e-01 PC=jacobi
[0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 18 with simple aggregation
[0] PCSetUp_GAMG(): 4) N=84, n data cols=6, nnz/row (ave)=82, 1 active pes
[0] PCSetUp_GAMG(): 5 levels, grid complexity = 1.43482


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